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Any number that is is a palindrome will always be a palindrome.
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Since a palindrome is just a number that reads the same way back and forth, the smallest palindrome would be 1. As there are an infinite number of palindromes (as you could just take any palindrome and simply place the same number in front of it and behind it, for example: 3, 939,99399,9993999,999939999, etc.), there is no biggest palindrome (infinity)