0

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. The "inequality" has a plural form by "inequalities". I would like to ask whether "equality" has plural form "equalities".

In my paper, I would like to write the following sentence.

We are concerned with the conditions under which two inequalities come to equality in the proof.

I'm not sure if that's right. Maybe the following is true

We are concerned with the conditions under which two inequalities come to equalities in the proof.

For another example, here are two inequalities.

$$2x\le 1$$ Equality occurs if and only if $x=\frac{1}{2}$.

$$5x\le 2$$ Equality occurs if and only if $x=\frac{2}{5}$.

I would like to say:

These two inequalities come to equalities(or equality?) when $x=\frac{1}{2}$ and $x=\frac{2}{5}$, respectively.

I want to replace "equality" with "equations", but I feel that equations and equality don't seem quite the same.

licheng
  • 2,266
  • 1
    Seems reasonable. There are plenty of articles/chapters listed here that use the plural. – user170231 Aug 15 '22 at 13:27
  • @user170231 Thanks a lot. I was worried that equality is not a countable noun. It seems that I am overthinking it. – licheng Aug 15 '22 at 13:33
  • @ancientmathematician Thank you very much. It was a slip. – licheng Aug 15 '22 at 13:34
  • 1
    I would use "corresponding equality/equalities", although I'd have to see more of what you're writing to know how to include this phrase. – Dave L. Renfro Aug 15 '22 at 13:40
  • 1
    I think this is called 'saturated'. As in "We are concerned with the conditions under which two inequalities are saturated in the proof." – Calvin Khor Aug 15 '22 at 13:46
  • 4
    I think your use of "equalities" is fine, but I'd change "come to" to "become". I also think "become equalities" is more common and more easily understood than "are saturated". – Andreas Blass Aug 15 '22 at 13:52

0 Answers0