STEP Prep Thread 2016 (Mark. II)

shamika whats ur opinion on the paper ?

Reply 1303

shamika

Original post by 1 8 13 20 42

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How do you have the paper? How do you even have the time for STEP (or are Warwick exams over)?

Reply 1304

shamika

Original post by Duke Glacia

shamika whats ur opinion on the paper ?

Don't have it so I can't say :frown:

Reply 1305

Original post by shamika

How do you have the paper? How do you even have the time for STEP (or are Warwick exams over)?

I have one more exam that I am fairly resigned to doing badly in as I missed all the lectures (and it is first year, and it is not core, and it isn't hugely contributive to my average, 8% of the year I think). A user sent it to me, I suppose I could/should upload it now that I think of it, if it isn't already up there, at some point, although I had just started actually doing a bit of revision.. :colonhash:

Reply 1306

shamika

Original post by 1 8 13 20 42

I have one more exam that I am fairly resigned to doing badly in as I missed all the lectures (and it is first year, and it is not core, and it isn't hugely contributive to my average, 8% of the year I think). A user sent it to me, I suppose I could/should upload it now that I think of it, if it isn't already up there, at some point, although I had just started actually doing a bit of revision.. :colonhash:

If you could upload it, that would be great. Good luck for the last exam!

Reply 1307

gasfxekl

8

Original post by 1 8 13 20 42

I have one more exam that I am fairly resigned to doing badly in as I missed all the lectures (and it is first year, and it is not core, and it isn't hugely contributive to my average, 8% of the year I think). A user sent it to me, I suppose I could/should upload it now that I think of it, if it isn't already up there, at some point, although I had just started actually doing a bit of revision.. :colonhash:

what's Warwick like

Reply 1308

Insight314

7

Original post by shamika

If you could upload it, that would be great. Good luck for the last exam!

Zacken also has it.

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Reply 1309

Zacken

OP

22

Original post by Insight314

Zacken also has it.

Didn't want to upload it without your permission. :tongue:

Reply 1310

Original post by shamika

If you could upload it, that would be great. Good luck for the last exam!

courtesy of Insight314, assuming it won't be minded

Original post by 1 8 13 20 42

Yes, that is in essence very similar just less wordy. I was just thinking one could do something rigorous/that doesn't rely on just saying "keep doing this until you stop" but considering STEPpers aren't supposed to have done set theory should probs be full marks for that kind of argument
(A well-ordering principle method for instance like the one used for integers in general)

Well, 'keep doing this until you stop' is actually valid. And this is more number theory than set theory.

For example, prime factorisation of the integers. We know a prime factorisation exists for every integer by the 'keep doing this until you stop' analogue. This is because no integer can be infinitely broken down into more and more factors - each time you decompose, you decrease the size of the integers you have, so decomposing infinitely would imply your 'integer' is infinite. If you wanted more convincing, suppose a prime factorisation exists for the first k integers, now if k+1 is prime leave it, else write it as a product of two integers between 1 and k+1. By the induction hypothesis, the product integers can be decomposed into primes, and so can k+1.

The only thing that 'keep doing this until you stop' does NOT prove is the uniqueness of prime factorisation, or the uniqueness of T-prime factorisation in our question. But the question doesn't care about that.

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(edited 7 years ago)

Reply 1312

Original post by Zacken

Didn't want to upload it without your permission. :tongue:

Now I feel guilty :frown:

Reply 1313

Zacken

OP

22

Original post by porridgepie

yes i thought my brain was being stupid again also the last part of 12 what on earth did they want, i got p(1)+.5p(2) but bit after when it asked for a generalisation of first parts or something

See the solution thread

Reply 1314

Original post by Ecasx

Well, 'keep doing this until you stop' is actually valid. And this is more number theory than set theory.

For example, prime factorisation of the integers. We know a prime factorisation exists for every integer by the 'keep doing this until you stop' analogue. This is because no integer can be infinitely broken down into more and more factors - each time you decompose, you decrease the size of the integers you have, so decomposing infinitely would imply your 'integer' is infinite. If you wanted something more convincing, suppose a prime factorisation exists for the first k integers, now if k+1 is prime leave it, else write it as a product of two integers between 1 and k+1. By the induction hypothesis, the product integers can be decomposed into primes, and so can k+1.

The only thing that 'keep doing this until you stop' does NOT prove is the uniqueness of prime factorisation, or the uniqueness of T-prime factorisation in our question. But the question doesn't care about that.

Posted from TSR Mobile

Oh yes it is valid. Perhaps rigorous is not the right word, sorry, maybe "clean".

Reply 1315

Ecasx

3

Original post by 1 8 13 20 42

Oh yes it is valid. Perhaps rigorous is not the right word, sorry, maybe "clean".

It's the easiest way to show a T-prime factorisation exists

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Reply 1316

Zacken

OP

22

Original post by shamika

If you could upload it, that would be great. Good luck for the last exam!

Here's a slightly more readable version: https://drive.google.com/open?id=0B6CGjKYdIeFEU0N4aF80WVNMYkk

Reply 1317