Mack
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 Sep 3 awarded Popular Question Jul 21 asked Restricting Binary Operator $*$ To A Subset Jul 17 awarded Notable Question Jul 15 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 15 asked Proving the Well-Ordering Property Jul 14 awarded Popular Question Jul 13 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 13 asked Proof About Division of Integers Jul 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. Jul 11 comment Inductive proof of inequality $a\le ab$ for nonnegative integers Yes, we are dealing with $\mathbb{N}$. So, my reasoning is correct? Jul 11 asked Inductive proof of inequality $a\le ab$ for nonnegative integers Jul 2 awarded Curious Jul 2 awarded Inquisitive Jun 25 comment Considering Vectors Geometrically You seem to be saying that the geometric picture follows from the way in which vector addition is defined, and the fact that $\mathbb{R}^n$ itself has a geometric interpretation? Jun 25 asked Considering Vectors Geometrically Jun 19 awarded Popular Question Jun 15 accepted Fourier's Heat Law In Integral Form Jun 15 awarded Popular Question