vb. 1. to have as a limit, especially (of a dependent variable) as the independent variable itself tends to a limit or infinity. 2. tend to infinity. to increase without limit. The value of an expression tends to infinity if it is such that for any number N, however large, a value of the expression can be found that is greater still. A limit of the function f(x) as x tends to infinity is a value to which the function becomes arbitrarily close as the independent variable increases without bound; this is written See limit.