0!=1 and 0^0=1, as you probably already know. Google it, if you don’t! Or use the Windows 7 calculator.
Should 0/0 also equal 1?
No. That would imply 0/0=5 or any other real number. This would spoil our game of math. Spoiled games are not very fun to play, therefore we must be very careful at defining the governing rules.
On occasion in the history of mathematics we weren’t as careful as we should have been. If only Pi would be two times as big as it is, life would be much simper. The so called number Tau movement wants to eradicate this error, Euler carelessly made when he defined Pi with the diameter instead of with the radius of a circle.
I am not even confident, that some other fundamental mathematical concepts are very good. Particularly those:
Oh yes, it’s blasphemy, I know, but I can’t help myself being suspicious about them all. Infinity is often under fire by finitists at least since Gauss. The Yablo paradox killed it in my view, by reproducing the Eubulides paradox without using self or circular referencing, but only with an infinite set of statements. Infinity is a dead horse, I don’t want to kick it anymore.
The next thing I am not that sure about is “set”. If there are x and y, what does the set of x any y mean? Is this is a necessary concept? I accept it as an abbreviation only.
And finally, zero. It has died a little already in physics. You can’t have zero temperature, you can’t have zero measurement error, you cant have zero entropy or energy. What’s the use of a concept with no use? Infinity on one, zero on the other side, have been on their way out of physics for some time now.
A whole new math could be required any day. With no infinities, no zero, no sets and much more complex than the versions we currently use.
We will have to update, I can’t wait!