# Infinitely Large Quantity

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Infinitely Large Quantity

in mathematics, a variable quantity that during a given process of variation becomes and remains greater in absolute value than any preas-signed number. The study of infinitely large quantities can be reduced to the study of infinitesimals, because if *y* is an infinitely large quantity, then its reciprocal *z* = 1/*y* is an infinitesimal. The fact that the variable y is an infinitely large quantity is written in the form limy = ∞. Here, the symbol ∞ (“infinity”) is only a conventional symbol indicating thaty is an infinitely large quantity. Another point of view is also possible according to which ∞ is an improper element added to the set of real numbers. Applicable to the function of an argument *x,* there is the following definition of the infinitely large quantity: the function *f(x),* defined in the neighborhood of the point *x*_{0}, is said to be infinitely large for *x* approaching *x*_{0}, if for any number *N* > 0 there exists a number δ > 0 such that for all *x* = *x*_{0}, ǀ*x* - *x*_{0}ǀ < δ, then the inequality ǀ*f(x)*ǀ > *N* is satisfied. This property is written in the form .

S. B. STECHKIN