- #1
*melinda*
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This is something that I think I should already know, but I am confused.
It really seems to me that the set of all real numbers, [itex]\Re[/itex] should be compact.
However, this would require that [itex]\Re[/itex] be closed and bounded, or equivalently,
that every sequence of points in [itex]\Re[/itex] have a limit point in [itex]\Re[/itex].
But I don't see how [itex]\Re[/itex] can be closed and bounded, unless we somehow decide that infinity is a real number.
So, are the real numbers compact?
thanks
It really seems to me that the set of all real numbers, [itex]\Re[/itex] should be compact.
However, this would require that [itex]\Re[/itex] be closed and bounded, or equivalently,
that every sequence of points in [itex]\Re[/itex] have a limit point in [itex]\Re[/itex].
But I don't see how [itex]\Re[/itex] can be closed and bounded, unless we somehow decide that infinity is a real number.
So, are the real numbers compact?
thanks