General expression/phrase for "less / greater than or equal to"?

Question

There is the expression / phrase "strict inequality" for mathematical expressions like -2 < 1 or 1/2 > - 1/2.

Is there an equivalent "short" expression where the equality is included in the relation? "Unstrict inequality" does not "feel" right.

"Inequality" seems too broad because it covers both cases: "less/greater than" " less/greater than or equal to".

I'm pretty sure the phrase nearly always used is "non-strict inequality". I think the phrase "lax inequality" is also used, quite often, but there is a danger of confusion with the name of the mathematician Peter Lax! — Calum Gilhooley, Jun 22 '19 at 16:52
Does this answer your question? If $<$ is a "strict inequality", what do we call $\leq$? — David K, Oct 09 '23 at 01:32

score 2 · Answer 1 · answered Jun 22 '19 at 16:18

2

$x\leq y$ is "$x$ is at most $y$".

$x\geq y$ is "$x$ is at least $y$".

answered Jun 22 '19 at 16:18

user10354138

user1110341 · Answer 2 · 2023-10-09T01:58:56.183

Weak Inequality! See Definition 1.3.3 at the top of page 9, in Hugo D. Junghenn's A Course in Real Analysis (2015).

The inequality a ≤ b is sometimes called weak inequality in contrast to strict inequality a < b.

See the first paragraph on page 28, of Mark Bridger's Real Analysis : A Constructive Approach Through Interval Arithmetic (2019).

It is also useful to have a notion of weak inequality, usually denoted ≤.

2 Answers2