The Proof is Trivial!

What point are you trying to make? That you're obnoxious? That is all that has been proven here tonight and scarcely needed more rigorous justification anyway.

He was JK.

*ba dum tsss*.

I'm not obnoxious, I was so clearly being facetious. I was referencing a similar conversation we had had a few weeks ago when you claimed this method was useless and no faster that hyperbolic substitutions. On what universe could that ever be misinterpreted?! I'm just having a laugh... making sarcastic comments... or is that not allowed?

Not sure what you thought I was doing but when I was posting alternative solutions to loads of peoples things but I wasn't doing it to be obnoxious or belittle anyones solutions or whatever you've got in your head If you bothered to read my foreword you would have seen that the set of integrals is from the MIT "integration bee" and, whilst the integrals weren't as difficult as the kind that are usually discussed on here, the intention was clearly to see how concise and compact we could get our solutions and so I don't see how having a little tease and showing you the alternative method has in any way upset you... though I suppose I should remember never to make a joke or say anything sarcastic again for fear that you might take it the wrong way

1) Given the number of negs your post has I'm clearly not the only person who found it/you obnoxious.

2) I did not state that solutions not using hyperbolics were not quicker, I stated that they were not as elegant (In reply to a similarly obnoxious suggestion that I should not be practising Mathematics because I didn't swoon at your method of doing things). Either way that is tangential to this matter.

3) I read the foreword, lots of integration. I did the integral in the way that I felt most comfortable approaching it and which was necessarily quicker for me because of that reason. The issue is also not with alternate solutions, and if you had read the thread you would have already seen bananarama suggest alternate subs to at least one integral I had already done. Similarly, if you'd simply said "why not try this sub, it's a little quicker" this discussion would not be happening.

4) This hasn't upset me - I'm not even one of the people contributing to the 10 negs (PRSOM). I've found it thoroughly obnoxious but I've got far thicker skin than to be particularly worried over an internet message.

(If you want to continue then PM me, we've clogged up this thread enough.)

The number of negative ratings I got is circumstantial given the fact that you taking it the wrong way made me look like an utter dick

Dude, I wasn't saying my way was better or more elegant or quick is was being sarcastically condescending, otherwise known as a

Is that the best paradox you can come up with?

Come on, there are way better ones than that old fogie.

(Enjoy)

After a long, arduous day in the life of Zakee, I pull out a tissue. Intrigued by the nature of the tissue and its fluffiness I lose myself in the procedure of tearing up a small part off of the tissue. I then take the larger portion of the tissue and tear that up, removing another small part off it. Now, I ask you the question, is this still a tissue? If I remove another small part of off the tissue, does is remain a tissue? If I continue this way, at what point does this object no longer act as a tissue?

When it has been contaminated by your bodily fluids

(Enjoy)

After a long, arduous day in the life of Zakee, I pull out a tissue. Intrigued by the nature of the tissue and its fluffiness I lose myself in the procedure of tearing up a small part off of the tissue. I then take the larger portion of the tissue and tear that up, removing another small part off it. Now, I ask you the question, is this still a tissue? If I remove another small part of off the tissue, does is remain a tissue? If I continue this way, at what point does this object no longer act as a tissue?

Can you not come up with one that's at least not two thousand plus a few hundred years old?

Intuitively, it seems to be the case that we know certain things with absolute, complete, utter, unshakable certainty. For example, if you travel to the Arctic and touch an iceberg,
you know that it would feel cold. These things that we know from experience are known through induction. The problem of induction in short; (1) any inductive statement (like the sun will
rise tomorrow)
can only be deductively shown if one assumes that nature is uniform. (2) the only way to show that nature is uniform is by using induction. Thus induction cannot be justified deductively.

Not a paradox, since it's possible to give solutions to the Problem of Induction that are sound but others may not necessarily agree with as a matter of opinion.

For example one could argue that facts obtained by induction on nature is only an approximation of the true facts (in the iceberg example, there is no inherent reason why you must have "absolute, complete, utter, unshakable certainty" on that the ice will feel cold, if one accepts that empirical results could always later be proved to be wrong). However those approximations are still useful as they give a quantified confidence level on which we take them to be truth.

Also this problem in no way detracts the validity of induction in mathematics, which has deductively sound interpretations.

Okay, here's a Millenium Prize problem:

How much wood would a woodchuck chuck
If a woodchuck could chuck wood?
He would chuck, he would, as much as he could,
And chuck as much as a woodchuck would
If a woodchuck could chuck wood?

The antecedent is impossible - woodchucks are ground animals and they burrow, instead of chucking wood, so the question is meaningless.

The antecedent is impossible - woodchucks are ground animals and they burrow, instead of chucking wood, so the question is meaningless.

Go and finish your dissertation and then be pedantic!

I have 9000 words to write before 14th of June.

Also this problem in no way detracts the validity of induction in mathematics, which has deductively sound interpretations.

Not a paradox, since it's possible to give solutions to the Problem of Induction that are sound but others may not necessarily agree with as a matter of opinion.

For example one could argue that facts obtained by induction on nature is only an approximation of the true facts (in the iceberg example, there is no inherent reason why you must have "absolute, complete, utter, unshakable certainty" on that the ice will feel cold, if one accepts that empirical results could always later be proved to be wrong). However those approximations are still useful as they give a quantified confidence level on which we take them to be truth.

Isn't that because mathematical induction is actually deduction haha?




Interestingly, I'm not sure if that is a solution the Problem of Induction: you still need to find a way to justify your confidence level, do you not? And how are you going to do that, if not by reasoning inductively in the first place? And for this you will need another confidence interval. And so on, ad infinitum.


There's a problem very closely linked to the problem of induction that I've always found fascinating and extremely frustrating. Again, I think it is a pretty old di/tri/multilemma, but it's always fun to think about!

Any valid argument must rely on either a circular chain of reasons, an infinite chain of reasons or on reasons that are not themselves justified.
An argument cannot be justified by a circular chain of reasons.
An argument cannot be justified by an infinite chain of reasons.
An argument cannot be justified if it relies upon unjustified assumptions.
Thus, no valid argument can be justified.