stevenvh
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 Apr18 comment Error in my proof? @egreg - I know it doesn't, but saying it does not apply doesn't count. For a rigorous proof he has to show it, otherwise his proof is incomplete, as you no doubt know. Apr18 answered Error in my proof? Apr18 comment Error in my proof? The exponent approaching zero is not sufficient. Think of $0^0$. Apr18 comment Mathematically, why was the Enigma machine so hard to crack? I agree with A.P. that the Rubik's Cube is not a good analogy. If you can memorize a small number of rules a human can solve any Cube configuration in seconds, despite its 10^20 possible combinations. A common PC will do it in a few microseconds. Jan9 awarded Yearling Jul2 awarded Curious Apr4 awarded Popular Question Apr2 awarded Nice Question Mar30 comment How to explain Real Big Numbers? @user136774 - That's why I say for most practical purposes. I remember a quote by a professor: "In theory the summation goes to infinity, but in practice infinity is five." When was the last time you needed Graham's Number in a real-life application? Or even 10^20? Mar28 awarded Popular Question Mar23 awarded Popular Question Jan22 accepted What are these sets of Pythagorean triples called? Jan11 asked What are these sets of Pythagorean triples called? Jan9 awarded Nice Question Nov22 awarded Popular Question Sep29 awarded Notable Question Aug7 awarded Yearling Feb19 awarded Notable Question Dec23 comment I have learned that 1/0 is infinity, why isn't it minus infinity? @millimoose - No, $\infty$ isn't a real number, I never said it was. But you can extend the reals to include $\infty$, that's the hyperreals, and then you can define operations which include reals and $\infty$. (Probably not a ring like I claimed earlier; none of the 4 basic operation has an inverse for $\infty$.) Dec22 comment I have learned that 1/0 is infinity, why isn't it minus infinity? @millimoose - The conclusion is correct inasmuch the limit can't be defined if left and right limit are different. That does not imply that it would be defined if they are equal. And $\infty$ + $\infty$ is $\infty$, by definition. $\infty$ is not a number, but that doesn't mean you can't define a ring for it. And operations with reals, like $\infty$ + r = $\infty$. The fact that $\infty$ + $\infty$ = $\infty$ is the reason why $\infty$ - $\infty$ is not defined; you can't find a result which is consistent with the definition for addition.