Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by underst... more Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by understanding how these disease will be formed, we may construct the corresponding statisticalcausalityregressionmodeloreventheartificialintelligenceone.Thismayhelpusdevelopthecorresponding drugs or vaccine. Indeed by applying the techniques as stated in one of my paper [11], one may even control the mutation or the evolution of the cancer or the COVID-19 virus whenever the Lorenz attractor or the Butterfly effects existing during the virus mutation process. This may be a breakthrough in the history of fighting against our human beings' nature enemy-virus.
How should one encourage “a positive and quality usage of ICT” among students? Earlier work (Lam,... more How should one encourage “a positive and quality usage of ICT” among students? Earlier work (Lam, June 2016) suggests that both “school and family partnership theory” and “mediation philosophy” are the keys to parents changing their attitude towards the handling of child ICT usage. Even so, what are the stages or processes of these transformation? This study reviews four models and theories (as described later) which predict people’s behavioural changes. Based on these, the author also recommends a “permeability model of changes” for depicting the parents’ alteration actions. Therefore, one can provide assistance, also known as – systemic therapy, immediately during the different stages or levels of change in the model. Hence, parents can successfully change their behaviour towards processing children’s ICT usage and in addition control these usage. Furthermore, this author also proposes that social, cultural and psychological factors of children’s ICT usage constitute a step approaching the philosophy of Digital Equity. These enhance the aim of the present research by – ultimately urging “a positive and quality usage of ICT” (Yuen et al., 2014: p.13) among students. The poor academic effects of using ICT for entertainment can therefore be eliminated. As a result, one can improve the scholarly achievements of students by using educational technology and can also bridge the digital divide in education.
The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-poin... more The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-point variable reduces to vector integral equations of Fredhom / Volterra type and is hard to solve. Translating it to scalar components equations would be an easier way of solving it. Here, the solution of the optimum path problem is recommended by connecting it with the Principle of minimum Energy Release (PMER). A lot of optimum path problems with path function E=cu 2 , where E is the released energy, u is the velocity, c is constant, can be solved by PMER, e.g., the Great Earthquake, the denotation of a nuclear weapon, the strategy of sports games. The one end-point fixed, the other end-point variable is studied for wing moving. High lights: The pulse-mode of nuclear denotation releasing energy is the same as Earthquake, Yun [1], shows that the derivative of wind velocity with respect to time in proportion to the derivative of temperature with respect to the track. Which conforms with the weather forecast in winter that strong wind companies with low temperature for cold wave coming, and also suits for the motion of mushroom cloud [2].
Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitute... more Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitutes a proof) to connect mathematics and Roger Penrose’s Three World Philosophy. Indeed, one can extend Roger’s Three World Philosophy to Wilber’s Spectrum of Consciousness which consists of four levels and nine stages. To delve deeper in the theory, one may propose that “Multiple World Philosophy” corresponds to the multiple number of types of infinity. This theory can then be applied to describe the complex multiple dimensions character for digital equity. In addition, it can depict the pictures about the interconnections between these dimensions, as there are also affiliations between these worlds. Therefore, “Multiple World Philosophy” is highly likely definitely to be a theory for solving mystery characters – multiple dimensions of Digital equity. The occurrence of Digital equity implies that we are emerging as an information based society. Thus, information-based ethics such as privacy, accuracy, property and accessibility should be included in local school curriculum. In such a case, the access or not access problem transcends to the problem of “Ethical usage in ICT device”. By understanding the philosophy of multiverse, one can overcome part of the gap it creates by applying the aforementioned strategy. In fact, one can only solve the problem by using multi-policies corresponding to different dimensions since digital equity employs a multi-dimensional philosophy. Therefore, schools, community resources, the government and private corporations should work together to develop a citizenry capability to participate in the present information age and to help settle the issue more effectively.
What does the term "Infinity" mean? There are mathematical, physical and metaphysical definitions... more What does the term "Infinity" mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scripting of the three philosophical foundations of mathematicsformalism, intuitionism and logicism-in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic definitions of infinity. These will correspond to Roger Penrose's Three World Philosophy and hence implies a quantum mind. By employing those special "rational proof" and set theory in this thesis, one may even build a real thinking computer. Indeed, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals' beauty fully. This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness. In the essence, this is what mathematics is: the science of researching the limitless. To conclude, the thinking machine's behind in this paper is very beautiful.
It is a common phenomenon that students using Information and Communication Tools. However, there... more It is a common phenomenon that students using Information and Communication Tools. However, there will be a great difference if one use it for entertainment or studying. One will named this as "Digital Capital for Education" and there is always a gap. To Overcome it, the author suggests that one should educate parents with school-family partnership and mediation philosophies so that parents can have an affirmative culture and attitude in handling their children's ICT usage at home properly. Hence, a positive and quality ICT usage among students will be encouraged and prevent negative academic effects.
One of the most important classes of Lie algebras is , which are the matrices with trace 0. The r... more One of the most important classes of Lie algebras is , which are the matrices with trace 0. The representation theory for has been an interesting research area for the past hundred years and in it the simple finite-dimensional modules have become very important. They were classified and Gelfand and Tsetlin actually gave an explicit construction of a basis for every simple finite-dimensional module. This paper extends their work by providing theorems and proofs, and constructs monomial bases of the simple module.
Original Research Article Mathematics surrounds us and has existed since ancient times. Numerals ... more Original Research Article Mathematics surrounds us and has existed since ancient times. Numerals originated from performing daily tasks that required conceptual counting. Later, symbols began to appear and had to be memorised. Over time, these formulas were simplified and transformed into notations. The collection of these symbols and notations became words, which gradually developed into a language. Indeed, mathematics can be used as a rational tool to link all kinds of knowledge. Throughout history, mathematics has been connected with all past human endeavours, and these achievements were composed to form different cultures. In addition, modern civilisation only has one common type of mathematics-in terms of symbols-to depict the world's natural phenomena. Therefore, mathematics is a common language for different nations and cultures. Taking a step further, this arguably implies that we have one creator, Christianity God-Jehovah.
Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by underst... more Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by understanding how these disease will be formed, we may construct the corresponding statisticalcausalityregressionmodeloreventheartificialintelligenceone.Thismayhelpusdevelopthecorresponding drugs or vaccine. Indeed by applying the techniques as stated in one of my paper [11], one may even control the mutation or the evolution of the cancer or the COVID-19 virus whenever the Lorenz attractor or the Butterfly effects existing during the virus mutation process. This may be a breakthrough in the history of fighting against our human beings' nature enemy-virus.
Lam, May, 2016 explained how mathematics as a subject is not just a technical one but also cultur... more Lam, May, 2016 explained how mathematics as a subject is not just a technical one but also cultural. As such, mathematical proofs and definitions are essential for students when learning the subject instead of simply numerical calculation. Hence, there needs to be a change in Hong Kong's local teachers' pedagogies. This author suggests three alternatives in how to teach mathematical philosophy through infinity. These are: 1. Teach the concept of limit in formalism through story-telling, 2. Use geometry to intuitively learn infinity through constructivism, and 3. Implement schematic stages for proof by contradiction Simultaneously, teachers should also be aware the difficulties among students in understanding different abstract concepts. These include: 1. Struggles in the concept " limit " , 2. Mistakes in intuitive computed infinity, 3. Puzzles in handling the method of " proof by contradiction " By doing so, teachers can provide the necessary support to pupils trying to comprehend and handle such difficult mathematical ideas. This finally leads to the transformations of students' belief (Rolka, et al., 2007). One can analyze them against the background of conceptual change. According to Davis (2001), " this change implies conceiving of teaching as facilitating, rather than managing learning and changing roles from the sage on the stage to a guide on the side ". As a consequence, there should hopefully be an improvement in Hong Kong' s Mathematical academic results.
Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitute... more Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitutes a proof) to connect mathematics and Roger Penrose's Three World Philosophy. Indeed, one can extend Roger's Three World Philosophy to Wilber's Spectrum of Consciousness which consists of four levels and nine stages. To delve deeper in the theory, one may propose that " Multiple World Philosophy " corresponds to the multiple number of types of infinity. This theory can then be applied to describe the complex multiple dimensions character for digital equity. In addition, it can depict the pictures about the interconnections between these dimensions, as there are also affiliations between these worlds. Therefore, " Multiple World Philosophy " is highly likely definitely to be a theory for solving mystery characters – multiple dimensions of Digital equity. The occurrence of Digital equity implies that we are emerging as an information based society. Thus, information-based ethics such as privacy, accuracy, property and accessibility should be included in local school curriculum. In such a case, the access or not access problem transcends to the problem of " Ethical usage in ICT device ". By understanding the philosophy of multiverse, one can overcome part of the gap it creates by applying the aforementioned strategy. In fact, one can only solve the problem by using multi-policies corresponding to different dimensions since digital equity employs a multi-dimensional philosophy. Therefore, schools, community resources, the government and private corporations should work together to develop a citizenry capability to participate in the present information age and to help settle the issue more effectively.
How should one encourage " a positive and quality usage of ICT " among students? Earlier work (La... more How should one encourage " a positive and quality usage of ICT " among students? Earlier work (Lam, June 2016) suggests that both " school and family partnership theory " and " mediation philosophy " are the keys to parents changing their attitude towards the handling of child ICT usage. Even so, what are the stages or processes of these transformation? This study reviews four models and theories (as described later) which predict people's behavioural changes. Based on these, the author also recommends a " permeability model of changes " for depicting the parents' alteration actions. Therefore, one can provide assistance, also known as – systemic therapy, immediately during the different stages or levels of change in the model. Hence, parents can successfully change their behaviour towards processing children's ICT usage and in addition control these usage. Furthermore, this author also proposes that social, cultural and psychological factors of children's ICT usage constitute a step approaching the philosophy of Digital Equity. These enhance the aim of the present research by – ultimately urging " a positive and quality usage of ICT " (Yuen et al., 2014: p.13)among students. The poor academic effects of using ICT for entertainment can therefore be eliminated. As a result, one can improve the scholarly achievements of students by using educational technology and can also bridge the digital divide in education.
What does the term " Infinity " mean? There are mathematical, physical and metaphysical definitio... more What does the term " Infinity " mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scription of the three philosophical foundations of mathematics – formalism, intuitionism and logicism – in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic aforementioned definitions of infinity. Indeed for example, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals' beauty fully (Nũńez, 2005). This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness (Maor, 1986). Actually, in essence this is what mathematics is: the science of researching the limitless.
There are various schools of Mathematical philosophy. However, none of them can founded our Mathe... more There are various schools of Mathematical philosophy. However, none of them can founded our Mathematics subject by itself only. At the same time, there are two types of mathematical proof styles: Dialectic and algorithm Mathematical proof. The relation between proof and philosophy is to study philosophical problems through building up mathematics model. Therefore proof is important to Hong Kong Secondary education. However, teachers should explain the connectivity between mathematics subjects and others like physics so that lessons will become more interesting rather than a technical one.
It is a common phenomenon that students using Information and Communication Tools. However, there... more It is a common phenomenon that students using Information and Communication Tools. However, there will be a great difference if one use it for entertainment or studying. One will named this as "Digital Capital for Education" and there is always a gap. To Overcome it, the author suggests that one should educate parents with school-family partnership and mediation philosophies so that parents can have an affirmative culture and attitude in handling their children's ICT usage at home properly. Hence, a positive and quality ICT usage among students will be encouraged and prevent negative academic effects.
Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by underst... more Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by understanding how these disease will be formed, we may construct the corresponding statisticalcausalityregressionmodeloreventheartificialintelligenceone.Thismayhelpusdevelopthecorresponding drugs or vaccine. Indeed by applying the techniques as stated in one of my paper [11], one may even control the mutation or the evolution of the cancer or the COVID-19 virus whenever the Lorenz attractor or the Butterfly effects existing during the virus mutation process. This may be a breakthrough in the history of fighting against our human beings' nature enemy-virus.
How should one encourage “a positive and quality usage of ICT” among students? Earlier work (Lam,... more How should one encourage “a positive and quality usage of ICT” among students? Earlier work (Lam, June 2016) suggests that both “school and family partnership theory” and “mediation philosophy” are the keys to parents changing their attitude towards the handling of child ICT usage. Even so, what are the stages or processes of these transformation? This study reviews four models and theories (as described later) which predict people’s behavioural changes. Based on these, the author also recommends a “permeability model of changes” for depicting the parents’ alteration actions. Therefore, one can provide assistance, also known as – systemic therapy, immediately during the different stages or levels of change in the model. Hence, parents can successfully change their behaviour towards processing children’s ICT usage and in addition control these usage. Furthermore, this author also proposes that social, cultural and psychological factors of children’s ICT usage constitute a step approaching the philosophy of Digital Equity. These enhance the aim of the present research by – ultimately urging “a positive and quality usage of ICT” (Yuen et al., 2014: p.13) among students. The poor academic effects of using ICT for entertainment can therefore be eliminated. As a result, one can improve the scholarly achievements of students by using educational technology and can also bridge the digital divide in education.
The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-poin... more The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-point variable reduces to vector integral equations of Fredhom / Volterra type and is hard to solve. Translating it to scalar components equations would be an easier way of solving it. Here, the solution of the optimum path problem is recommended by connecting it with the Principle of minimum Energy Release (PMER). A lot of optimum path problems with path function E=cu 2 , where E is the released energy, u is the velocity, c is constant, can be solved by PMER, e.g., the Great Earthquake, the denotation of a nuclear weapon, the strategy of sports games. The one end-point fixed, the other end-point variable is studied for wing moving. High lights: The pulse-mode of nuclear denotation releasing energy is the same as Earthquake, Yun [1], shows that the derivative of wind velocity with respect to time in proportion to the derivative of temperature with respect to the track. Which conforms with the weather forecast in winter that strong wind companies with low temperature for cold wave coming, and also suits for the motion of mushroom cloud [2].
Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitute... more Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitutes a proof) to connect mathematics and Roger Penrose’s Three World Philosophy. Indeed, one can extend Roger’s Three World Philosophy to Wilber’s Spectrum of Consciousness which consists of four levels and nine stages. To delve deeper in the theory, one may propose that “Multiple World Philosophy” corresponds to the multiple number of types of infinity. This theory can then be applied to describe the complex multiple dimensions character for digital equity. In addition, it can depict the pictures about the interconnections between these dimensions, as there are also affiliations between these worlds. Therefore, “Multiple World Philosophy” is highly likely definitely to be a theory for solving mystery characters – multiple dimensions of Digital equity. The occurrence of Digital equity implies that we are emerging as an information based society. Thus, information-based ethics such as privacy, accuracy, property and accessibility should be included in local school curriculum. In such a case, the access or not access problem transcends to the problem of “Ethical usage in ICT device”. By understanding the philosophy of multiverse, one can overcome part of the gap it creates by applying the aforementioned strategy. In fact, one can only solve the problem by using multi-policies corresponding to different dimensions since digital equity employs a multi-dimensional philosophy. Therefore, schools, community resources, the government and private corporations should work together to develop a citizenry capability to participate in the present information age and to help settle the issue more effectively.
What does the term "Infinity" mean? There are mathematical, physical and metaphysical definitions... more What does the term "Infinity" mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scripting of the three philosophical foundations of mathematicsformalism, intuitionism and logicism-in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic definitions of infinity. These will correspond to Roger Penrose's Three World Philosophy and hence implies a quantum mind. By employing those special "rational proof" and set theory in this thesis, one may even build a real thinking computer. Indeed, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals' beauty fully. This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness. In the essence, this is what mathematics is: the science of researching the limitless. To conclude, the thinking machine's behind in this paper is very beautiful.
It is a common phenomenon that students using Information and Communication Tools. However, there... more It is a common phenomenon that students using Information and Communication Tools. However, there will be a great difference if one use it for entertainment or studying. One will named this as "Digital Capital for Education" and there is always a gap. To Overcome it, the author suggests that one should educate parents with school-family partnership and mediation philosophies so that parents can have an affirmative culture and attitude in handling their children's ICT usage at home properly. Hence, a positive and quality ICT usage among students will be encouraged and prevent negative academic effects.
One of the most important classes of Lie algebras is , which are the matrices with trace 0. The r... more One of the most important classes of Lie algebras is , which are the matrices with trace 0. The representation theory for has been an interesting research area for the past hundred years and in it the simple finite-dimensional modules have become very important. They were classified and Gelfand and Tsetlin actually gave an explicit construction of a basis for every simple finite-dimensional module. This paper extends their work by providing theorems and proofs, and constructs monomial bases of the simple module.
Original Research Article Mathematics surrounds us and has existed since ancient times. Numerals ... more Original Research Article Mathematics surrounds us and has existed since ancient times. Numerals originated from performing daily tasks that required conceptual counting. Later, symbols began to appear and had to be memorised. Over time, these formulas were simplified and transformed into notations. The collection of these symbols and notations became words, which gradually developed into a language. Indeed, mathematics can be used as a rational tool to link all kinds of knowledge. Throughout history, mathematics has been connected with all past human endeavours, and these achievements were composed to form different cultures. In addition, modern civilisation only has one common type of mathematics-in terms of symbols-to depict the world's natural phenomena. Therefore, mathematics is a common language for different nations and cultures. Taking a step further, this arguably implies that we have one creator, Christianity God-Jehovah.
Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by underst... more Cancer or COVID-19 virus can be serious harmful diseases to our human beings. However, by understanding how these disease will be formed, we may construct the corresponding statisticalcausalityregressionmodeloreventheartificialintelligenceone.Thismayhelpusdevelopthecorresponding drugs or vaccine. Indeed by applying the techniques as stated in one of my paper [11], one may even control the mutation or the evolution of the cancer or the COVID-19 virus whenever the Lorenz attractor or the Butterfly effects existing during the virus mutation process. This may be a breakthrough in the history of fighting against our human beings' nature enemy-virus.
Lam, May, 2016 explained how mathematics as a subject is not just a technical one but also cultur... more Lam, May, 2016 explained how mathematics as a subject is not just a technical one but also cultural. As such, mathematical proofs and definitions are essential for students when learning the subject instead of simply numerical calculation. Hence, there needs to be a change in Hong Kong's local teachers' pedagogies. This author suggests three alternatives in how to teach mathematical philosophy through infinity. These are: 1. Teach the concept of limit in formalism through story-telling, 2. Use geometry to intuitively learn infinity through constructivism, and 3. Implement schematic stages for proof by contradiction Simultaneously, teachers should also be aware the difficulties among students in understanding different abstract concepts. These include: 1. Struggles in the concept " limit " , 2. Mistakes in intuitive computed infinity, 3. Puzzles in handling the method of " proof by contradiction " By doing so, teachers can provide the necessary support to pupils trying to comprehend and handle such difficult mathematical ideas. This finally leads to the transformations of students' belief (Rolka, et al., 2007). One can analyze them against the background of conceptual change. According to Davis (2001), " this change implies conceiving of teaching as facilitating, rather than managing learning and changing roles from the sage on the stage to a guide on the side ". As a consequence, there should hopefully be an improvement in Hong Kong' s Mathematical academic results.
Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitute... more Previous work from Lam, August, 2016 shows that infinity can be used as a bridge (i.e. constitutes a proof) to connect mathematics and Roger Penrose's Three World Philosophy. Indeed, one can extend Roger's Three World Philosophy to Wilber's Spectrum of Consciousness which consists of four levels and nine stages. To delve deeper in the theory, one may propose that " Multiple World Philosophy " corresponds to the multiple number of types of infinity. This theory can then be applied to describe the complex multiple dimensions character for digital equity. In addition, it can depict the pictures about the interconnections between these dimensions, as there are also affiliations between these worlds. Therefore, " Multiple World Philosophy " is highly likely definitely to be a theory for solving mystery characters – multiple dimensions of Digital equity. The occurrence of Digital equity implies that we are emerging as an information based society. Thus, information-based ethics such as privacy, accuracy, property and accessibility should be included in local school curriculum. In such a case, the access or not access problem transcends to the problem of " Ethical usage in ICT device ". By understanding the philosophy of multiverse, one can overcome part of the gap it creates by applying the aforementioned strategy. In fact, one can only solve the problem by using multi-policies corresponding to different dimensions since digital equity employs a multi-dimensional philosophy. Therefore, schools, community resources, the government and private corporations should work together to develop a citizenry capability to participate in the present information age and to help settle the issue more effectively.
How should one encourage " a positive and quality usage of ICT " among students? Earlier work (La... more How should one encourage " a positive and quality usage of ICT " among students? Earlier work (Lam, June 2016) suggests that both " school and family partnership theory " and " mediation philosophy " are the keys to parents changing their attitude towards the handling of child ICT usage. Even so, what are the stages or processes of these transformation? This study reviews four models and theories (as described later) which predict people's behavioural changes. Based on these, the author also recommends a " permeability model of changes " for depicting the parents' alteration actions. Therefore, one can provide assistance, also known as – systemic therapy, immediately during the different stages or levels of change in the model. Hence, parents can successfully change their behaviour towards processing children's ICT usage and in addition control these usage. Furthermore, this author also proposes that social, cultural and psychological factors of children's ICT usage constitute a step approaching the philosophy of Digital Equity. These enhance the aim of the present research by – ultimately urging " a positive and quality usage of ICT " (Yuen et al., 2014: p.13)among students. The poor academic effects of using ICT for entertainment can therefore be eliminated. As a result, one can improve the scholarly achievements of students by using educational technology and can also bridge the digital divide in education.
What does the term " Infinity " mean? There are mathematical, physical and metaphysical definitio... more What does the term " Infinity " mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scription of the three philosophical foundations of mathematics – formalism, intuitionism and logicism – in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic aforementioned definitions of infinity. Indeed for example, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals' beauty fully (Nũńez, 2005). This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness (Maor, 1986). Actually, in essence this is what mathematics is: the science of researching the limitless.
There are various schools of Mathematical philosophy. However, none of them can founded our Mathe... more There are various schools of Mathematical philosophy. However, none of them can founded our Mathematics subject by itself only. At the same time, there are two types of mathematical proof styles: Dialectic and algorithm Mathematical proof. The relation between proof and philosophy is to study philosophical problems through building up mathematics model. Therefore proof is important to Hong Kong Secondary education. However, teachers should explain the connectivity between mathematics subjects and others like physics so that lessons will become more interesting rather than a technical one.
It is a common phenomenon that students using Information and Communication Tools. However, there... more It is a common phenomenon that students using Information and Communication Tools. However, there will be a great difference if one use it for entertainment or studying. One will named this as "Digital Capital for Education" and there is always a gap. To Overcome it, the author suggests that one should educate parents with school-family partnership and mediation philosophies so that parents can have an affirmative culture and attitude in handling their children's ICT usage at home properly. Hence, a positive and quality ICT usage among students will be encouraged and prevent negative academic effects.
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