nathanpoppelreiter.blogspot.com

Chasing the Logos

Tuesday, November 23, 2010. A Proof Concerning Zorn's Lemma. I sat on this proof for a week and a half before I finally cracked it. Claim: Every chain in a partially ordered set is included in some maximal chain if Zorn's Lemma holds. Be a poset, let P(X). Pretty sweet little proof, a lot simpler than my early trials, which involved, first, recursion and, second, a recursion-like action on the empty. Hope you enjoyed this as much as I enjoyed working on it. Truly the joy of why I do these things. Claim: ...

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Chasing the Logos | nathanpoppelreiter.blogspot.com Reviews

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Tuesday, November 23, 2010. A Proof Concerning Zorn's Lemma. I sat on this proof for a week and a half before I finally cracked it. Claim: Every chain in a partially ordered set is included in some maximal chain if Zorn's Lemma holds. Be a poset, let P(X). Pretty sweet little proof, a lot simpler than my early trials, which involved, first, recursion and, second, a recursion-like action on the empty. Hope you enjoyed this as much as I enjoyed working on it. Truly the joy of why I do these things. Claim: ...

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2 proof let x

3 no comments

4 labels posets

5 proofs

6 zorns lemma

7 labels continuity

8 limits

9 proofs

10 1 comment

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Chasing the Logos | nathanpoppelreiter.blogspot.com Reviews

https://nathanpoppelreiter.blogspot.com

Tuesday, November 23, 2010. A Proof Concerning Zorn's Lemma. I sat on this proof for a week and a half before I finally cracked it. Claim: Every chain in a partially ordered set is included in some maximal chain if Zorn's Lemma holds. Be a poset, let P(X). Pretty sweet little proof, a lot simpler than my early trials, which involved, first, recursion and, second, a recursion-like action on the empty. Hope you enjoyed this as much as I enjoyed working on it. Truly the joy of why I do these things. Claim: ...

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nathanpoppelreiter.blogspot.com

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Chasing the Logos: November 2010

http://nathanpoppelreiter.blogspot.com/2010_11_01_archive.html

Tuesday, November 23, 2010. A Proof Concerning Zorn's Lemma. I sat on this proof for a week and a half before I finally cracked it. Claim: Every chain in a partially ordered set is included in some maximal chain if Zorn's Lemma holds. Be a poset, let P(X). Pretty sweet little proof, a lot simpler than my early trials, which involved, first, recursion and, second, a recursion-like action on the empty. Hope you enjoyed this as much as I enjoyed working on it. Truly the joy of why I do these things.

2

Chasing the Logos: July 2010

http://nathanpoppelreiter.blogspot.com/2010_07_01_archive.html

Tuesday, July 27, 2010. Some Proofs on Limits and Continuity. Here are a couple of proofs that I think are nice. By nice, I mean, I like how I proved the claim because the proof is concise, clear, and rigorous. Let f:R- R be a continuous function. For all r in Q, let f(r)=0. Claim: f(x)=0 for all x in R. This one is pretty facile, but I still liked how I proved it. Let f:D- R, with c in D', and lim(x- c)f(x)=L 0. Claim: There is V=N*(c, ß): f(x) 0, for all x in R. Pf: Pick ß such that ß. Claim: The natur...

3

Chasing the Logos: March 2010

http://nathanpoppelreiter.blogspot.com/2010_03_01_archive.html

Monday, March 15, 2010. Good Morning, Proof! Here is the third proof (or, rather, set of proofs) I'll be expected to know. Properties of Elements and Subgroups Under Homomorphisms. Let G and G' be groups, where P maps G into G', and H is a subgroup of G. Claim: P maps the identity of G to the identity of G'. Claim: P(g n)=[P(g)] n. Claim: If g is finite, then P(g) divides g . Pf: Let g =n. Then, g n=e. Then, e=P(e)=P(g n)=[P(g)] n. Then, by Thm 4.2, P(g) divides n= g . qed. Claim: KerP is a subgroup of G.

4

Chasing the Logos: Some Proofs on Limits and Continuity

http://nathanpoppelreiter.blogspot.com/2010/07/some-proofs-on-limits-and-continuity.html

Tuesday, July 27, 2010. Some Proofs on Limits and Continuity. Here are a couple of proofs that I think are nice. By nice, I mean, I like how I proved the claim because the proof is concise, clear, and rigorous. Let f:R- R be a continuous function. For all r in Q, let f(r)=0. Claim: f(x)=0 for all x in R. This one is pretty facile, but I still liked how I proved it. Let f:D- R, with c in D', and lim(x- c)f(x)=L 0. Claim: There is V=N*(c, ß): f(x) 0, for all x in R. Pf: Pick ß such that ß.

5

Chasing the Logos: proofs to come soon...

http://nathanpoppelreiter.blogspot.com/2010/05/proofs-to-come-soon.html

Monday, May 3, 2010. Proofs to come soon. My internet has been down at my house for a bit now, but you can expect some cool proofs to come soon. Look for a proof to Gauss's Lemma - it's pretty sexy. Posted by Nathan Poppelreiter. Subscribe to: Post Comments (Atom). Study Guide 1 for Ring and Field Theory, Midterm 2. Proofs to come soon.

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Chasing the Logos

Tuesday, November 23, 2010. A Proof Concerning Zorn's Lemma. I sat on this proof for a week and a half before I finally cracked it. Claim: Every chain in a partially ordered set is included in some maximal chain if Zorn's Lemma holds. Be a poset, let P(X). Pretty sweet little proof, a lot simpler than my early trials, which involved, first, recursion and, second, a recursion-like action on the empty. Hope you enjoyed this as much as I enjoyed working on it. Truly the joy of why I do these things. Claim: ...

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