I’m sorry, but you don’t understand the concept of infinity. At all. You don’t understand how it works in analysis or set theory. You never “arrive” at infinity. There isn’t an “infinity-th” digit on 0.999…, there isn’t a number “infinity” on the real number line, and at any point where a function might colloquially be valued at infinity, it is considered “not defined”. There is almost no point in mathematics where is it considered valid to insert “infinity” into your equation - the only point where it is more than colloquially valid is as the x_0 for a limes, or as a value for a limes. Strictly speaking, while we all can generally grasp what c is in 10^-infinity = c (it’s zero), this usage makes mathematicians cry. It’s simply not valid. Infinity, as a concept, is something you approach. It’s not a number.
It’s very simple - “limes of x -> x_0 = infinity” is a meaningful mathematical statement; “x = infinity” is not. That’s how we distinguish between them. :rolleyes:
Ah, another value that doesn’t actually exist. Please, either prove that the infinitesimal exists and define it, or shut up about it. This is something you basically invented out of whole cloth, and have still neither defined nor provided any explanation of how it is not equal to zero. In fact, using set theory, it has been proven to you several times that according to your definitions, Z is not a real number, Z+1=inf makes no sense whatsoever, and your infinitesimal is zero. You have offered neither rebuttal nor anything to back up your unsupported and unsupportable claims in the first place.
Do you even understand the concept of limes? Like, at all? Dude, seriously. Why don’t you do yourself a favor and stop talking about mathematics when you obviously have no clue about it? You can’t even perform a long division of
1/3!
No, you showed how you think infinity is usually thought to be accessed. And you were wrong. Almost fractally wrong, come to think of it.
So is Z not a real number, or is infinity a real number?
The answer to that calculation is infinity. But only because of the limes.
…What
This is a word salad of non-sequiturs and missed points. No, we do not need to find a place for infinity. It’s not on the number line. That the number line tends towards infinity simply means that it goes on forever, and that you can get as large as you want. It is never equal to infinity - infinity is not on the line. But regardless of how meaningless this proof is, the fact of the matter remains that If Z element of R, Y element of R, X not element of R, then Z+Y = X IS FALSE.
X is not element of R.