Use of the word “convergent”

This question is for people who know some mathematics.

Is it correct to say

The sequence is convergent to 0.

Normally we say: The sequence converges to 0.


Without going into whether it is correct or not (I think it’s acceptable), I can tell you why mathematicians use it. Sometimes, we want to emphasise the value of the limit. In such cases, we say “This sequence converges to 0” or “The limit of this sequence is 0”. But sometimes, when we’re more concerned with the analysis of the sequence (whether it is a convergent sequence, or divergent, or what), we want to emphasise the fact that it converges, rather than its limit. In such cases, instead of saying

This sequence is convergent, and its limit is 0″


This sequence is convergent, and it converges to 0″

we (or some mathematicians) use a shortcut and say, equivalently,

“This sequence is convergent to 0.”

Source : Link , Question Author : TCL , Answer Author : ShreevatsaR

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