If "not greater than" is equivalent to "less than or equal to" then is "less than" equivalent to "less than or equal to"?
2026-03-31 22:51:43.1774997503
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Similar signs of ineqaulities
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No, I think you've slightly misunderstood the logic here.
Suppose we have two numbers, a and b. Obviously either a is greater than b, a is equal to b, or a is less than b. This is called 'trichotomy', meaning 'three options', and is a very important rule.
Therefore, if a is not greater than b then either a is equal to b or a is less than b.
Similarly, if a is not less than b then either a is equal to b or a is greater than b.
'a is less than b' and 'a is less than or equal to b' are not equivalent statements, because 2 is not less than 2 but 2 is less than or equal to 2. Similarly, 'a is less than b' and 'a is not greater than b' are also not equivalent statements, because '2 is less than 2' is false but '2 is not greater than 2' is true.
$2 < 2$ is a false statement but $2 \le 2 $ is a true statement, they are not equivalent.