- #1
brntspawn
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Homework Statement
If S[tex]\subset[/tex]R is finite and non-empty, then S has a maximum.
Can someone look over this? I struggled a bit in my first proof class, which is why I am asking for help, so I really am unsure if this is right at all.
Let S={1}
So 1[tex]\in[/tex]R such that for all x[tex]\in[/tex]S, 1[tex]\geq[/tex]x
So 1 is an upper bound for S
1[tex]\in[/tex]S, so by definition 1=max S
Let S={m+1}
Then m+1>m for all m[tex]\in[/tex]S
So m+1 is an upper bound for S
Since m+1[tex]\in[/tex]S, then by definition m+1=max S
Therefore if S[tex]\subset[/tex]R is finite and non-empty, then S has a maximum.