31 questions linked to/from Do odd imaginary numbers exist?
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### Is infinity an odd or even number?

My 6 year old wants to know if infinity is an odd or even number. His 38 year old father is keen to know too.
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### Why is $9$ special in testing divisiblity by $9$ by summing decimal digits? (casting out nines)

I don't know if this is a well know fact but I have observed that every number no matter how large that is equally divided by $9$, will equal $9$ if you add all the numbers it is made from until there ...
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### How to avoid arithmetic mistakes?

When dealing with several numbers and long equations, it's common to make careless arithmetic mistakes that give the wrong answer. I was wondering if anyone had tips to catch these mistakes, or even ...
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### Proof by contradiction: $r - \frac{1}{r} =5\Longrightarrow r$ is irrational?

Prove that any positive real number $r$ satisfying: $r - \frac{1}{r} = 5$ must be irrational. Using the contradiction that the equation must be rational, we set $r= a/b$, where a,b are positive ...
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### Are these two quotient rings of $\Bbb Z[x]$ isomorphic?

Are the rings $\mathbb{Z}[x]/(x^2+7)$ and $\mathbb{Z}[x]/(2x^2+7)$ isomorphic? Attempted Solution: My guess is that they are not isomorphic. I am having trouble demonstrating this. Any hints, as to ...
I'll quickly go over my understanding of it: If a number $n^2$ is even, then $n$ is even. The contrapositive is that is that if $n$ is not even (odd), then $n^2$ must also be not be even (be odd). ...