Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it. You can extend those sets to include infinity - but then you have to extend the definition of …

Aug 11, 2012 · Essentially, you gave the answer yourself: "infinity over infinity" is not defined just because it should be the result of limiting processes of different nature. I.e., since such a …

Apr 28, 2016 · $\begingroup$ Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like …

Dec 25, 2017 · When we use straightforward approach, we get $$ \frac{\infty+1}{\infty} = \frac{\infty}{\infty} $$ In the process of investigating a limit, we know that both the numerator …

Infinity is not a natural number, or a real number: there should be no confusion about that. We can use infinity as the upper limit of an integral as shorthand to say that all the reals greater than …

Your title says something else than "infinity times zero". It says "infinity to the zeroth power". It is also an indefinite form because $$\infty^0 = \exp(0\log \infty) $$ but $\log\infty=\infty$, so the …

Dec 18, 2012 · $\begingroup$ "Or that the infinity of the even numbers is the same as that of the natural numbers." - not necessary. This depends on your definitions. I would argue the infinity …

Infinity does not lead to contradiction, but we can not conceptualize $\infty$ as a number. The issue is similar to, what is $ + - \times$, where $-$ is the operator. The answer is undefined, …

May 14, 2017 · The infinity can somehow branch in a peculiar way, but I will not go any deeper here. This is just to show that you can consider far more exotic infinities if you want to. Let us …

$\begingroup$ In terms of set theory, it is true that for any infinite power K:k+k=kk=k. note that for a=0 : ak=0 and not infinity $\endgroup$ – Belgi Commented Mar 19, 2012 at 19:58