Difference between sup and max

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They only differ when the set on which they operate has an infinite number of elements:

If X has a finite number of elements, then $$\sup (x\ :\ x\in X)=\max (x\ :\ x\in X)$$ Because the sup is then simply attained at some point in X. However, this is not necessarily the case, as the following example will illustrate: Let $X=(0,1) $. Then $\sup (X)=1$, while 1 is not a member of X. $\max (X) $ does not exists in this case. Hope this helps :)

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yoko
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yoko

i like numbers.

Updated on August 01, 2022

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  • yoko
    yoko over 1 year

    I am working at some Fuzzy-Logic and I am having my problems with the inferece. While using the generalised modus ponens you are using this formula

    μB'(y) := sup{min(μA'(x),min(μA(x),μB(y))) | x∈X} for y∈Y

    My Question is, where is the Difference between the min/max Operators and the sup/inf Operators? Aren't they both just for finding the largest/smallest Value?