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I have two non-empty sets A and B wich is bounded above by R.

Then I'm tasked with proving that

[tex]sup(A \cup B) = max(sup A, sup B) [/tex]

which supposedly means that [tex]sup(A \cup B) [/tex] is the largest of the two numbers sup A and sup B.

Can this then be written as [tex]sup(A) < sup(A \cup B) [/tex] and [tex]sup(B) < sup(A \cup B)[/tex] ???

Can this then be proven by showing that [tex]sup(A) < sup(A \cup B) [/tex] is true?

Or am I totally on the wrong path here??

/Bob

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