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"We encourage children to read for enjoyment, yet we never encourage them to 'math' for enjoyment. We teach kids that math is done fast, done only one way and if you don't get the answer right, there's something wrong with you. You would never teach reading this way." - Rachel McAnallen

"Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition." - Morris Kline


4h
revised Prove: $A \cap(B\cup C^*)=(A\cap B)\cup C^*$
added 13 characters in body
4h
revised Prove: $A \cap(B\cup C^*)=(A\cap B)\cup C^*$
added 13 characters in body
6h
comment Prove: $A \cap(B\cup C^*)=(A\cap B)\cup C^*$
Not quite; see my answer. Edit: In particular, you've got the inequality backwards.
6h
revised Prove: $A \cap(B\cup C^*)=(A\cap B)\cup C^*$
added 458 characters in body
6h
answered Prove: $A \cap(B\cup C^*)=(A\cap B)\cup C^*$
7h
comment What do these symbols mean? One looks like an inverse “T”, another looks like ^
It might mean orthogonal complement, depending on what kind of an object $U_k$ is.
9h
comment Is the completeness theorem for first-order logic relative to one's choice of set theory?
Peter, would it be fair to say that the completeness theorem cannot be expressed in first-order arithmetic?
1d
comment Could someone explain aleph numbers?
In a couple of hours I'll be done with this assignment and I'll have a go at explaining them.
2d
accepted Showing the right half of the unit hyperbola is a complete metric space.
2d
comment (If exists) a set of all ordinals that set is an ordinal?
"An ordinal is a transitive set of transitive sets" not quite; its a hereditarily transitive set. This basically means "transitivity all the way down."
Oct
22
comment Are there mathematical contexts where “finite” implicitly means “nonzero?”
"Are there mathematical contexts in which zero is definitively considered to be not finite?" Dear Lord, I hope not!
Oct
22
comment Showing the right half of the unit hyperbola is a complete metric space.
@Travis, sorry, I don't understand the difference. What is a pullback in this context? I am somewhat familiar with pullbacks from category theory, but my knowledge of Reimannian geometry is rather primitive.
Oct
22
revised Showing the right half of the unit hyperbola is a complete metric space.
added 71 characters in body
Oct
22
comment Showing the right half of the unit hyperbola is a complete metric space.
@Travis, I mean this; it is not just the restriction of the usual metric to $\mathrm{im}(f)$.
Oct
22
asked Showing the right half of the unit hyperbola is a complete metric space.
Oct
21
comment Notation for non-empty subset
@Ronny, I know what you mean. Another option would be: "Consider non-empty $A \subseteq S$."
Oct
21
revised Notation for non-empty subset
edited body
Oct
21
comment Notation for non-empty subset
I don't like this kind of thing (not downvoting or anything, just expressing my opinion). There's nothing more confusing than reading: "Now consider $\emptyset \neq A \subset S$."
Oct
21
answered Notation for non-empty subset
Oct
21
accepted Are $e : 1 \rightarrow X$ and $\mathrm{id}_X : X \rightarrow X$ the only operations of $\mathsf{Grp}$ that are homomorphisms?