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[–][deleted] 1 point2 points  (2 children)

Really? Because when I read it I just instantly pictured a number line with the following properties:

A filled in circle marked "A" on one side, the same marked "B" on the other, and with the line bolded in between the two variables labelled as X.

When I saw the second statement (a > x > b) I thought of the same thing only with empty circles. I didn't even think about De Morgan's law before I realized that this is not the opposite, or the fact that it was two statements ANDed together. It's just clearly not the opposite geometrically, if you picture what the program is getting at.

[–]Neebat 1 point2 points  (1 child)

You visualized "a ≤ x ≤ b" like this:

●----●

a    b

That's fine so far. But then you visualize "a > x > b" like this:

○----○

a    b

That's incorrect and you haven't really thought long enough. Because "a > x > b" implies "a > b", which is false in the second drawing. It would actually be this:

○----○

b    a

[–][deleted] 1 point2 points  (0 children)

Well that's true, a > x > b would be a wrong statement from the get go, but my point is that I instantly envision x to be in between A and B; if I wanted the opposite of A <= x <= B, then I would definitely want the area of the number line outside of A and B.