I suppose you could ask what happens to 1/x as x tends to -∞ .
eg 1/-1000 < 1
1/-1000000000 < 1
etc.
It looks like 1/x tends to zero from below (from the left) as x tends to -∞ and we know that 0 < 1.
So I suppose the answer to your question (ignoring the rules for a moment) is YES.
Bob
]]>and is 1/-∞ < 1 too?
]]>The number line is usually shown running left to right with (say) 2 to the left of 3 etc.
The symbol < (which we read as "less than") actually means "is to the left of", so -4 < -3 etc. As -∞ is the 'leftmost' place you could have on the line* -∞ < x for all x on the line.
* But as you cannot get to this place it is (strictly) not on the line.
Bob
]]>Yes. -∞ < 1
The list of integers is
-∞, -∞ + 1, -∞ + 2, -∞ + 3, .........., -3, -2, -1, 0, 1, 2, 3, ..........., ∞
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