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Dedekind cuts Anonymous Thu Mar 28 10:24:51 2013 No.5644145 [Reply] [Original]

Is there something inherently wrong/childish/trivial/silly/babbyish about constructing the real numbers through Dedekind cuts?

I will elaborate, but will refrain for now as not to introduce bias.

/sci/ related pic is unrelated

Anonymous Thu Mar 28 10:27:20 2013 No.5644148

>>5644145
Since reals don't exist I don't spend a lot of time thinking about "constructing" them, but cauchy sequences seem to have the nice property that they in essence abstract over a metric which could yield reals or p-adics depending. Is the same true of cuts?

>>	Anonymous Thu Mar 28 10:27:35 2013 No.5644149 I don't think so. Being rigorous is not negative.

>>	Anonymous Thu Mar 28 10:28:35 2013 No.5644152 File: 18 KB, 427x232, 04strogatz1-custom3[1].jpg [View same] [iqdb] [saucenao] [google] >>5644148 >>5644148 are you even trying brah

>>	Anonymous Thu Mar 28 10:37:21 2013 No.5644166 >>5644152 > not answering the question

OP Thu Mar 28 10:41:21 2013 No.5644174

Ok, I guess I should just elaborate now.

Basically, there is this kid in my analysis class that is always mumbling to himself, chuckling and shaking his head at things the professor says, and one of his favorite lines is how Rudin or "the Soviets" wouldn't use something so boring as cuts (our class doesn't use Rudin as a text).

He's fat, has hair down to his waist, smells weird, wears old tshirts with dolphins and new age shit like crystals and Mayan gods or something (sorry, I can't really explain), and when the professor decides to ask him if he has something to add to the discussion he declines. I'm fairly certain he has a solid F in the class as I've passed a couple of his exams back to him.

I know I shouldn't pay attention to people like this but stuff creeps into the back of your mind.

>>	Anonymous Thu Mar 28 10:44:06 2013 No.5644179 >>5644174 um im pretty sure rudin DOES use them ... sounds like you found someone that posts to /v/ or /x/

>>	Anonymous Thu Mar 28 10:46:20 2013 No.5644183 >>5644179 >>5644174 Yeah I don't get it, Rudin uses dedekind cuts too...

>>	Anonymous Thu Mar 28 10:50:50 2013 No.5644187 >>5644148 There is wisdom amid your lunacy. Cuts are cute, but the Cauchy sequence approach seems more generally applicable. See definition of "completeness."

>>	OP Thu Mar 28 10:51:20 2013 No.5644189 >>5644179 >>5644183 I see. Maybe I'll call him on it sometime. Thanks.

>>	Anonymous Thu Mar 28 11:27:08 2013 No.5644243 >>5644189 Dedekind cuts are an appendix to the first chapter of the most recent edition and the very beginning of the very first chapter in previous editions....

>>	Anonymous Thu Mar 28 11:42:13 2013 No.5644258 I prefer cuts over sequences from an aesthetic sense, but I suppose the sequences are more useful in other areas.

>>	Anonymous Thu Mar 28 12:09:49 2013 No.5644293 File: 96 KB, 500x400, mgm.jpg [View same] [iqdb] [saucenao] [google] >>5644258

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