1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Upper bound question

  1. Dec 28, 2011 #1
    This calc book that I am reading uses words like "upper bound" and "sup" alot when proving theorems. I have never heared these terms before so it makes it hard for me to understand the proofs.

    I think it has to deal with max's values of a graph: For example given a set S of all elements c in a ≤ c ≤ b would the the upper bound in the following graph in [a,b] be c? and also c = Sup S...
    is this correct?

    Attached Files:

  2. jcsd
  3. Dec 28, 2011 #2
    Upper bound is any value that is greater than or equal to all the values in a set.

    sup is short for supremum, the least upper bound of a set of numbers. The range of a function might be such a set. The supremum is not necessarily a member of the set: for example, the supremum of the range of the sigmoid function [tex]\frac{1}{1+e^{-x}}[/tex] is 1, but that is not a value of the function. 1 is an upper bound to this function, but so are 2, 100 and 100!2
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook