5 ms·
Infinity is not a number, it's the absence of a limit.
by w0mbat 3y ago
Infinity is not a number, it's the absence of a limit.
- MetaWhirledPeas 3y agoNaN
- cubefox 3y agoYeah. Though the defenders of transfinite (ordinal and cardinal) numbers do in fact assert that there are many infinite numbers, such as aleph zero or omega. They are just usually somewhat embarrassed about this and therefore only talk about "ordinals" or "cardinals". It's like trying to hide that you drink beer by saying you merely drink lagers and ales.
- deleted 3y ago[deleted]
- mkup 3y agoAbsense of limit is not always an infinity, e.g. for sequence (-1)^n. Even if sequence is unbounded, it does not always converge to infinity, e.g. n^((1+(-1)^n)/2): 1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 14, 1, 16, 1, 18, 1, 20 ... Convergence of sequence x(n) to infinity by definition is: for each real number ε>0 there exists a natural number N(ε) such that for every number n≥N(ε) we have |x(n)|>ε.
- cubefox 3y agoWhat would be x in case of the natural numbers?