leehuan's All-Levels-Of-Maths SOS thread (6 Viewers)

[leehuan]

Delta is the smaller of the two. The importance of this is that if we make something less than delta, it'll be simultaneously less than 2 and eps/4.

Oh right. So you're kinda picking an actual number to restrict delta to be less than first, before generalising it for all epsilon?

 

[InteGrand]

Oh right. So you're kinda picking an actual number to restrict delta to be less than first, before generalising it for all epsilon?

Well essentially the motivation behind making delta to be less than 2 is to deal with the |x+1| in the |x+1||x-1| stage.

When we're at |x+1||x-1|, we want to make this less than eps.

We can control |x-1| directly, since it's less than delta, so we can make it less than eps/4 say (we could also do a lot of other things, like eps/6, or whatever; the choice for delta is non-unique).

If we could just force |x+1| to be less than 4, we'd be done, since then we'd have |x+1||x-1| be less than 4*eps/4 = eps.

The idea is that when we're "near" 1 (since x is approaching 1), |x+1| is going to be bounded; it can't get too big.

Precisely speaking, if we restrict our consideration to be within 2 units of 1, then |x+1| will always be less than 4.

So by taking delta to be smaller than* 2 AND smaller than eps/4, we get |x+1| < 4 AND |x-1| < eps/4.

The way to make these simultaneous "smaller thans" for delta is to make it the min of those two things, and then let |x-1| be less than delta.

* delta actually doesn't need to be smaller than them, just equal to them. Then by letting |x-1| be less than this delta, we get |x+1| < 4 and |x-1| < eps/4, which is what we wanted.

 

[Drongoski]

I still don't fully know what I'm doing. Another demo please, but on a trivial statement this time



All I can say is



I have no clue on the method

You have stated, but not shown the existence of the delta required.

It is interesting to note that for a relatively simple function y = x^2, to show that the limit of y as x goes to 1 is 1 can be so hard - for most students being exposed to the epsilon-delta definition for the first time.

leehuan: you are lucky to have a very consummate and selfless helper in InteGrand to come to your aid every time. I wish BoS could give him a medal for his unfailing and tireless contribution, which were it to happen, he would promptly decline.

 

[leehuan]

leehuan: you are lucky to have a very consummate and selfless helper in InteGrand to come to your aid every time.

Yes I know I am. I'm always grateful of anyone's work and most noteworthy him (especially since he's almost always the one helping everyone else out too)

And the question was basically requiring a method.

 

[Drsoccerball]

leehuan: you are lucky to have a very consummate and selfless helper in InteGrand to come to your aid every time. I wish BoS could give him a medal for his unfailing and tireless contribution, which were it to happen, he would promptly decline.

He's the real MVP.

 

[Nailgun]

Most common message on BoS

"You must spread some Reputation around before giving it to InteGrand again."

 

[Trebla]

This thread will be closed shortly.

After careful consideration, it was decided that user specific threads will no longer be allowed (whether they be one user helping or one user asking for help). We have noticed that the first few threads have spawned multiple others, which is not desirable in the spirit of being an open community. The last thing we want is the Maths forums being full of "User X Maths Help" threads.

You are encouraged to post separate questions in separate threads, though keep in mind a lot of the questions that I have seen so far have been answered before so I suggest to actually do a search first to see if it hasn't been answered already in past threads (which is easier to do when there is a specific thread for a specific question or topic rather than a general user specific thread).

 

[Nailgun]

rip

 

[eyeseeyou]

This thread will be closed shortly.

After careful consideration, it was decided that user specific threads will no longer be allowed (whether they be one user helping or one user asking for help). We have noticed that the first few threads have spawned multiple others, which is not desirable in the spirit of being an open community. The last thing we want is the Maths forums being full of "User X Maths Help" threads.

You are encouraged to post separate questions in separate threads, though keep in mind a lot of the questions that I have seen so far have been answered before so I suggest to actually do a search first to see if it hasn't been answered already in past threads (which is easier to do when there is a specific thread for a specific question or topic rather than a general user specific thread).

How will we get help then if our teachers aren't gonna help?

 

[leehuan]

How will we get help then if our teachers aren't gonna help?

Make our own threads. So long as Trebla isn't against me making 5 threads a day during desperate times I'm not too bothered. (Unless of course the next question allows for some thread revival for the sake of grouping)

But the reason I made my thread was because my questions were beyond the HSC level and I didn't anticipate many people would have interest in what I was doing. Whilst I did get the idea off someone else, their's had actually been merged into the Marathon thread. (Ironically, that also re-reshaped my view of the marathon - I originally thought it was for all sorts of questions, then I realised that marathon questions were meant to be really hard for an average student, then I'm back to thinking it's for all sorts of question).

I never exactly intended for people to follow suit on what I did in terms of HSC level questions as a result of that prior merge.

 

[Trebla]

How will we get help then if our teachers aren't gonna help?

Post a new thread for any question you may have? That's how it has been always been (and should be) done ever since the Maths forums existed.

 

[Green Yoda]

Post a new thread for any question you may have? That's how it has been always been (and should be) done ever since the Maths forums existed.

Would making a "Prelim 2016 Maths Thread" be considered alright?

 

[eyeseeyou]

Would making a "Prelim 2016 Maths Thread" be considered alright?

Bingo Rathin you genius ily

 

[Trebla]

Would making a "Prelim 2016 Maths Thread" be considered alright?

That is fine as it is not user specific.