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.
Limit of a function (the Dirichlet function) has no limit at any x-coordinate.
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.
Continuous or discrete variable A continuous variable is one which can take on infinitely many, uncountable values.