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Feb22-09, 06:16 PM
no, i don't think sqrt(2) exists. This is my reason: sqrt(2) is just a symbol for it's decimal representation which is 1.414213562..., and the decimal places continue on infinitely.
So, if we will never reach the last digit in the decimal places for sqrt(2), how can we multiply it by itself.
It's the same logic that goes with the fact that we can't multiply any number by infinity. For example, 0 x infinity is an ideterminate form, because although we know logically that you will get 0 if you keep multiplying 0s, we will never finish multiplying 0 infinitely many times so we say that it is undefined.
In other words, sqrt(2) by definition is a number that you multiply by itself in order to get 2. However, we will never be able to get that number so it should be undefined for the same reason that infinity is undefined.
So tell me, what does "exist" mean? Do you think 2 exists? How so? Is there a realm of numbers where 2 exists but sqrt(2) doesn't?
what about sqrt(2) km? Does that exist?