For questions specifically concerning models of arithmetic (which could be Peano Arithmetic, the first-order theory of the natural numbers, or some other system) which differs from the standard model by the existence of nonstandard numbers.
A non-standard model of arithmetic is, usually, a model of (first-order) Peano Arithmetic which differs from the standard model $\mathbb{N}$, specifically by containing nonstandard numbers. As the standard numbers $0,1,2,\ldots$ are an initial segment of every model of Peano Arithmetic, these nonstandard numbers must be greater than every standard number.
