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/sci/ - Science & Math

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1162999 No.1162999 [Reply] [Original]

sup /sci/

I had the worst exam of my life today, feels bad man. Chances are that this exam could mean I get a 2:2.

Here's a part of it:

Prove that for any non zero ordinal <span class="math"> \alpha [/spoiler] , there exists a natural number k, non zero natural numbers <span class="math"> n_0 , n_1 , n_2 , \ldots , n_{k-1} [/spoiler] , and ordinals <span class="math"> \delta_0 > \delta_1 > \ldots > \delta_{k-1} [/spoiler] such that

<span class="math"> \alpha = \sum_{i=0}^{k-1} \omega^{\delta_i} n_i [/spoiler]

Is this representation unique?

So, yeh was a bitch of an exam question (was only the last part of one of 4 questions mind) but I thought it was quite interesting and worth posting.

On the plus side, people were crying after the exam, that's always fun to see.

Cheer me up /sci/ .

>> No.1163021

What the fuck subject is that?

>> No.1163015
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1163015

>>1162999
Hey, at least your not a faggot (a engineer)!

>> No.1163034

>>1163015

haaa, that's true.

>>1163021

Set Theory :(

>> No.1163030

looks like number theory

definitely some obscure mathematics course that would provide zero benefit to real-world scenarios

so on that note, OP is a faggot

>> No.1163036

>>1163030

well done for showing how little you actually know.

on that note. NO U

>> No.1163041

>>1162999
You found that hard...

What the fuck?

>> No.1163083
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1163083

OP, what school you go to?

>> No.1163086

>>1163034
Well, thank you for letting me know I will never, ever study Set Theory.

>> No.1163134

>>1163083

i go to oxford. you? you got exams at the moment as well?

>> No.1163140

Jesus fucking christ, OP.
What level of education are you currently pursuing?

If that's the type of shit you have to understand for computer science, I'm fucked.

>> No.1163151

>>1163140

This was set theory. Mathematics degree, although some of my friends taking maths/comp-sci joint schools took this as an option. they hated this exam as well.

So yeh, this material wouldn't be compulsory on any computer science course.

>> No.1163156

>>1163140
thats basic undergrad math FAGGOT!

>> No.1163174

>>1163151
Ah, I see.

What type of career are you hoping for after you obtain your degree?

>> No.1163186

>>1163134

Which college and year bro? I'm Worcester year 1 CS.

>> No.1163189

>>1163174

I didn't go to uni to get a career.

inb4 shitstorm about math grads working at mcdonalds.

>> No.1163196

>>1163186

Nice, you got functional/design and analysis of algorithms programming on tuesday? I do, it's my last exam, can't wait to finish.

>> No.1163200
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1163200

>>1163030
>he doesn't realise that pure maths always ends up being relevant to physical sciences eventually

>> No.1163228

Hey guys calculus looked like a foreign language before you ever took a calculus course. Just sayin.

>> No.1163231

LOL at oxford-fags still doing exams.

All Cambridge exams are already over. Most subjects finished last week or earlier.

>> No.1163259

>>1163231

I'd rather be a leper than a tab

>> No.1163263

>>1163228
Hold the fuck up!!! I GOT THIS SHIT!

I took AP Calculus in senior year of high school, bitches.
Failed both semesters with a 55. Booyah!

>> No.1163283

>>1163231

You mirin the new league tables bra?

http://extras.timesonline.co.uk/stug/universityguide.php

>> No.1163333

>>1162999

Wait, so every ordinal has a (possibly unique) power series representation, with ordinals as the powers?

Does anyone know if this is true or have sources to verify? Seems a bit weird to me.

>> No.1163390 [DELETED] 

>>1163333

i couldn't find any sources, but my proof went as follows:
(i) prove that for all non zero ordinals <span class="math"> \alpha [/spoiler] , there exists an ordinal <span class="math"> \delta [/spoiler] such that

<span class="math"> \omega^delta \leq \alpha < \omega^{\delta^{+}}[/spoiler]

(ii) Prove then that there exists a none zero natural number n, and an ordinal <span class="math"> \zeta [/spoiler] such that <span class="math"> \zeta < omega^{\delta} [/spoiler] and <span class="math"> \alpha = \omega^{\delta} \cdot n + \zeta [/spoiler]

(iii) apply this recursively to zeta, got a power series.

>> No.1163393

=i=0k−1ini

>> No.1163405

>>1163333
>>1163333

i couldn't find any sources, but my proof went as follows:
(i) prove that for all non zero ordinals <span class="math"> \alpha [/spoiler] , there exists an ordinal <span class="math"> \delta [/spoiler] such that

<span class="math"> \omega^{\delta} \leq \alpha < \omega^{\delta^{+}}[/spoiler]

(ii) Prove then that there exists a none zero natural number n, and an ordinal <span class="math"> \zeta [/spoiler] such that <span class="math"> \zeta < \omega^{\delta} [/spoiler] and <span class="math"> \alpha = \omega^{\delta} \cdot n + \zeta [/spoiler]

(iii) apply this recursively to zeta, got a power series.

>> No.1163416

>>1163283
You know every global university league table rates Cambridge higher than oxford by at least 4 places, right?

>> No.1163458

>>1163283
you would have failed this exam even if you went to cambridge

>> No.1163537

>>1163393

wut

>> No.1163575

>>1162999

I wouldn't have a clue how to go about solving that. Never really done much set theory, though. More of an applied mathematics guy myself.

Are you a third year?

>> No.1163599

>>1163575

yup. although this is my fourth year of uni (i retook a year)

i done mostly applied courses this year:

applied pdes
mathematical biology/ecology
quantum mechanics & quantum theory/quantum computing

i used to be all about the pure, but this year kinda turned me off it ( I dropped representation theory and geometry of surfaces)

>> No.1163639

>>1163599

Yeah, this year put me off pure. Especially Group Theory. All the modules I've chosen for next year are stuff like Special Relativity, Fluid Dynamics, Quantum Information, as well as a few computing modules.

>> No.1163648

>>1163639

Doing a degree in maths has taught me that I prefer physics. Or, mathematical physics, at least.

>> No.1163679

>>1163405
How do you know the recursion terminates after a finite number of power series terms?

>> No.1163697

>>1163679

i don't! it's where i would have dropped marks, but i waved hands a bit.

any ideas?

>> No.1165431

that's cantors notation for ordinals you fucking idiot. do you know nothing? seriously, you deserved to fail

>> No.1165453

>On the plus side, people were crying after the exam, that's always fun to see.

I think I love OP.

>> No.1165518

>>1163405
Use induction hypothesis in the last step.