Science

Any incredibly tiny value that you can imagine will be larger than what separates them as the infinite series 9/10 + 9/100 + 9/1000 + 9/10000 + ... continues FOREVER.

If there can never be a value that separates their difference, they're equal.

Just like 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... equals 1, as an INFINITE series.

With each iteration of that particular series, the difference between the summation and 1 equals the last term added. But no matter what incredibly small number we consider, we will eventually reach a term 1 / (2^n) in the series which is even smaller. Thus, no such difference can be found and they're equal.

Without this kind of reasoning, simple formulas for what integrals equal in calculus wouldn't exist. Nobody says, "This algebraic formula ALMOST equals this integral."