Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Apostol: infinity as finite point

  1. Nov 4, 2011 #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...
     
  2. jcsd
  3. Nov 4, 2011 #2
    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.
     
  4. Nov 4, 2011 #3

    ohhh i see...so basically R, by not including infinity, contains only finite points, and the opposite is true of R*. thanks Steve!
     
  5. Nov 4, 2011 #4

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    "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 [ ].
     
    Last edited: Nov 4, 2011
  6. Nov 4, 2011 #5
    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
     
  7. Nov 8, 2011 #6
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook