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Apr
18
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.
Apr
18
answered Error in my proof?
Apr
18
comment Error in my proof?
The exponent approaching zero is not sufficient. Think of $0^0$.
Apr
18
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.
Jan
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Jul
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Apr
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Apr
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Mar
30
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?
Mar
28
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Mar
23
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Jan
22
accepted What are these sets of Pythagorean triples called?
Jan
11
asked What are these sets of Pythagorean triples called?
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Feb
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Dec
23
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 $\infty$.)
Dec
22
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.