Definition: Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which …

2012年8月11日 · I know that $\infty/\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for

2016年4月28日 · Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like $\lim_ {n\to\infty} (1+x/n)^n,$ or is it just a …

For infinity, that doesn't work; under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$. So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember …

2012年12月18日 · I understand that there are different types of infinity: one can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers. Or that the …

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 the arithmetic …

3 Infinity does not lead to contradiction, but we can not conceptualize ∞ ∞ as a number. The issue is similar to, what is + − × + ×, where − is the operator. The answer is undefined, because + + and × × …

In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form. Your title says something else than "infinity times zero". It …

2017年5月14日 · 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 then turn to …

2017年12月25日 · 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 and denominator …