Learn English – the term for an integer one larger than a given integer

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I'm looking for a concise term to say a number must be exactly one higher than a previous number.

None of "subsequent", "incremental", or "next" seem to convey the restriction that it must be contiguous to the previous number. "Contiguous" does not convey that it must be larger rather than smaller.

Is there a specific term for this or am I going to have to use a phrase like "contiguous to and larger than"?

Best Answer

The number that's one greater than a given natural number n is called the successor of n. See the Peano axioms, which are a standard foundational definition of the set of natural numbers.

This terminology strictly is only defined for natural numbers, but I think it can be safely extended to integers without confusion.