1/3 is not strictly equal to 0.333...

instead, it cannot be strictly equal in decimal notation. We're taught that anything can be rendered in decimal, but for some things it's not really accurate and is simply more of a cheat.

unfortunately the cheat also works towards convincing some people that 0.999... = 1, even though this is not essentially the case. This has to do with seemingly-infinite repetition. In the case of rendering 1/3 as 0.333... using the cheat, it makes enough sense that this specific rendering of 0.333... approximating 1/3 specifically, times 3, would produce 0.999..., and that 1/3 *3 = 1.

however, this does not hold true for something like

[math]\sum_{n}^{\infty}\frac{1}{2^n}[/math] which intends to strictly produce a 0.999... result. This calculus however "uses" "infinity", which rationally isn't actual infinity but is instead seemingly infinite.

to quickly define the difference between infinite and seemingly-infinite, both are technically shortened from their results and there is an unimaginable degree of accuracy should one continue with calculation, so "seemingly-infinite" is more like a realnumber (infinity-1). There is no countable proof for either infinity or seemingly-infinite, so in the same regard there is no strong evidence an (infinity-1) cannot exist as a real number too long to intelligently do any math with, which would give it the same relevant property as straight-up "infinity" does. In all, anything that is described as infinite is more likely than not simply seemingly-infinite.