is negative infinity to positive infinity the same as all real numbers
Infinity In mathematics, "infinity" is often treated as a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as either a natural or a real number.
1 + 2 + 3 + 4 + ⋯ which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
Exponentiation Any nonzero number raised to the 0 power is 1:[11]
Limit of a function (the Dirichlet function) has no limit at any x-coordinate.
Limit of a function respectively. If these limits exist at p and are equal there, then this can be referred to as the limit of f(x) at p. If the one-sided limits exist at p, but are unequal, there is no limit at p (the limit at p does not exist). If either one-sided limit does not exist at p, the limit at p does not exist.
Convergent series A series is convergent if the sequence of its partial sums   { S 1  ,   S 2  ,   S 3  , … }  {\displaystyle \left\{S_{1},\ S_{2},\ S_{3},\dots \right\}}  tends to a limit; that means that the partial sums become closer and closer to a given number when the number of their terms increases. More precisely, a series converges, if there exists a number   ℓ  {\displaystyle \ell }  such that for any arbitrarily small positive number   ε  {\displaystyle \varepsilon } , there is a (sufficiently large) integer   N  {\displaystyle N}  such that for all   n ≥   N  {\displaystyle n\geq \ N} ,