"For every number a not equal to 0, there exists a number b such that ab = 1."

I am aware of a related post on the use of "such that", I am not sure how the explanations there fit in to the use of "such that" in the above sentence.

  • 2
    In mathematics, “such that ...” means “for which the following property holds: ...” Sep 24, 2021 at 8:23

1 Answer 1


This is consistent with the following definition of such from Lexico

  1. such — as/that Of the type about to be mentioned.
    the wound was such that I had to have stitches

The "type about to be mentioned" is numbers that fit the criteria "ab = 1"

  • I don't see why Lexico explains the use of "such" in my sentence. Lexico lists "such" as a determiner, a predeterminer, or a pronoun. If "such" is a determiner or a predeterminer, then what is the corresponding noun/pronoun in the sentence? If "such" is a pronoun, what is "such" referring to? Every example in Lexico involving "such that" is of the form "... is/was such that...", a pattern that my sentence does not fit into.
    – aamu
    Sep 27, 2021 at 20:53
  • The noun is a condition that b fits. I added one of the example sentences that is kind of similar outside the mathematical context.
    – Barmar
    Sep 27, 2021 at 20:57
  • 2
    This isn't an explanation; it's a translation. And it's correct. What would count as an "explanation"? A bunch of logical formulae? A history of the so/such ... that S construction? Jun 26, 2022 at 16:23

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