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accepted The role of 'arbitrary' in proofs
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asked Restricting Binary Operator $*$ To A Subset
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comment Proving the Well-Ordering Property
Why not? You just do the same comparison that I did in the case of two and three elements.
Jul
15
comment Proving the Well-Ordering Property
But I am proving that $S$ is well-ordered, and eventually, after having added enough elements to $S$, won't I get that $S = \mathbb{Z}^+$? So, because the two sets are equivalent, any property that one thing possess, the other thing must possess, right? In particular, $S$ possess the property that it has a minimal element; so, by the equality, $\mathbb{Z}^+$ has a minimal element.
Jul
15
comment Proving the Well-Ordering Property
Why isn't it clear what $S$ is supposed to be? Didn't I specify that it was some subset of $\mathbb{Z}^+$, and only contained the two elements $a,m \in \mathbb{Z}^+$? Isn't that clear enough? All I am doing in my proof is continually adding more elements from the set $\mathbb{Z}^+$ into $S$. How is that any less clear than what you said about $A$ in your post?
Jul
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asked Proving the Well-Ordering Property
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comment Proof About Division of Integers
That is what I figured, that the problem was concerned with existence, but I was not exactly certain.
Jul
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asked Proof About Division of Integers
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11
comment Inductive proof of inequality $a\le ab$ for nonnegative integers
I have another question, then. How does one prove that the sum of two positive integers yields a number greater than the individual numbers.