proving that zero is in the middle

shahar

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Jul 19, 2018
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How I prove that zero is between the plus infinity to the negative infinity?
 
How I prove that zero is between the plus infinity to the negative infinity?

Can you explain why you are asking, and what you mean by this? What sort of proof would be acceptable (that is, what axioms or theorems would you accept)?

In one sense, +infinity and -infinity are not numbers at all, so you can't really say 0 is between them; but it is obvious that (on the affinely extended real number line, where they are defined) -infinity < 0 < +infinity. This depends on how you define +infinity and -infinity.

If you are claiming that 0 is the average of +infinity and -infinity, that statement has no meaning; averaging only applies to numbers. And there is no way to say that 0 is the exact middle of the number line; any number can be taken as the middle.

So, what are you asking for?
 
Can you explain why you are asking, and what you mean by this? What sort of proof would be acceptable (that is, what axioms or theorems would you accept)?

In one sense, +infinity and -infinity are not numbers at all, so you can't really say 0 is between them; but it is obvious that (on the affinely extended real number line, where they are defined) -infinity < 0 < +infinity. This depends on how you define +infinity and -infinity.

If you are claiming that 0 is the average of +infinity and -infinity, that statement has no meaning; averaging only applies to numbers. And there is no way to say that 0 is the exact middle of the number line; any number can be taken as the middle.

So, what are you asking for?
Thanks for your remarks.
 
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