Apostol: infinity as finite point

  • #1
I found a torrent online of Apostol's "Mathematical Analysis" 1st edition and I think I found a typo, or whoever scanned the book cut off the edge a bit...

Apostol writes that the extended real number system R* is denoted by [-∞, +∞] while the regular real number system R is denoted by (-∞, ∞). Then he says "The points in R are called 'finite' to distinguish them from the 'infinite' points +∞ and -∞. " Shouldn't it read that the points in R* are finite, not the points in R? Because if you include infinity in the interval, you are treating it as a finite point?

The "R" is the sentence that I quoted above is a the very edge of the page so it could be that the scanner of the book cut off the " * " accidentally, but I just want to confirm...
 

Answers and Replies

  • #2
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I found a torrent online of Apostol's "Mathematical Analysis" 1st edition and I think I found a typo, or whoever scanned the book cut off the edge a bit...

Apostol writes that the extended real number system R* is denoted by [-∞, +∞] while the regular real number system R is denoted by (-∞, ∞). Then he says "The points in R are called 'finite' to distinguish them from the 'infinite' points +∞ and -∞. " Shouldn't it read that the points in R* are finite, not the points in R? Because if you include infinity in the interval, you are treating it as a finite point?

The "R" is the sentence that I quoted above is a the very edge of the page so it could be that the scanner of the book cut off the " * " accidentally, but I just want to confirm...
I think he means that the points in R (as a subset of R*) are called finite. So in R*, the numbers 3, -6, and pi are finite. +/-infinity are infinite.
 
  • #3
I think he means that the points in R (as a subset of R*) are called finite. So in R*, the numbers 3, -6, and pi are finite. +/-infinity are infinite.

ohhh i see...so basically R, by not including infinity, contains only finite points, and the opposite is true of R*. thanks Steve!
 
  • #4
AlephZero
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"Infinty" is not included in the open interval [itex](-\infty,\infty)[/itex]. An open interval does not contain its end points.

Be careful about the notation for an open inteval ( ) and a closed interval [ ].
 
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  • #5
"Infinty" is not included in the open interval [itex](-\infty,\infty)[/itex]. An open interval does not contain its end points.

Be careful about the notation for an open inteval ( ) and a closed interval [ ].
thanks but I do know the difference between open and closed interval.
R* is denoted by closed interval [-∞,∞] and R by open. I am assuming you thought that there cannot be a thing as [-∞, ∞] ? Thats what I thought too until I read the above mentioned book lol
 
  • #6
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can you tell me where did you find the torrent for the first edition cause i can only found the second one and there is some proof wich is only in the first one
Thank you
 

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