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The concerned reader might wonder how it is possible to assert that there is _one_ correct definition of an extension of the factorial function to the real/complex numbers. Why is …

The story of what happens if we defined, for example, 1/0 = 0 is a little more complicated. I will include it because it is sufficiently interesting. Equality of fractions is defin…

Standard mathematical systems of arithmetic do not permit a reasonable definition of 1/0. Mathematicians define equality of fractions by stating that a/b = c/d if and only if a·d =…

It should be true for every y that is allowed in the denominator. That is how fractions are handled in higher math. (Either called "localization" or "ring of fractions").

You could look for a math history book (such as "An Imaginary Tale" by Nahin) or something like the Princeton Companion to Mathematics or frankly any other popular math book writte…

There are two very good ways of understanding Euler's formula and one is the "circular motion" explanation given by another comment. Both are very similar. The other is that "multi…

This is obviously not a completely serious question but it is definitely looks like a question someone might ask when learning about complex numbers for the first time. The answer …

For maximum safety you should assume your adversary knows which character set your password comes from. Frankly, there are few reasons not to assume this.

I imagine that a lot of people responding to this do not realize how abstract modern pure mathematics is. The number theory that makes up the basis of cryptography was established …

Its pretty standard in the US (at least in the fields I am familiar with) that if you quit a PhD program you can still leave with a Master's if you've been in the program for long …

Of course this quote also suggests that maybe people who go in to PhD programs have higher rates of mental health issues. I would definitely argue that PhD programs are both bad fo…

Isn't he also trying to say that perhaps the bias that some women have against male doctors might also contribute to the statistic? In other words, women heart attack patients migh…

Does anyone else think technology has a lot to do with this? Recall the experiment where a rat is placed in a cage with a "pleasure button" that stimulates reward centers in its br…