/sci/ - Science & Math » Thread #10407413

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Redpill me on limits

Anonymous Fri 22 Feb 05:58:31 2019 No.10407413 View Reply Original Report

Quoted By: >>10407434 >>10407445 >>10407539 >>10407677 >>10407691

My calc 1 prof skipped the rigorous definition of limit section. I've read the epsilon delta chapter a few times but don't feel as if its intuitive the same way the rest of the course is. It still feels like magic, or a cheat, though I don't believe it is.

Anonymous

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Anonymous Fri 22 Feb 2019 06:27:51 No.10407434 Report

Quoted By: >>10407442

>>10407413
>feels like magic
the whole point of e-d is you don't have to understand wtf the function is doing in the box, just that the fucker stays in the box & the box keeps getting smaller

Anonymous

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Anonymous Fri 22 Feb 2019 06:34:13 No.10407442 Report

Quoted By: >>10407476

>>10407434
Does that also imply continuity in the box, or do I have to prove that first?

Anonymous

Anonymous Fri 22 Feb 2019 06:35:44 No.10407445 Report

Quoted By:

>>10407413
try to apply the epsilon-delta idea to things that don't converge
like say, the harmonic series

Anonymous

Anonymous Fri 22 Feb 2019 06:51:35 No.10407476 Report

Quoted By:

>>10407442
Do you know the definition of continuity?

Anonymous

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Anonymous Fri 22 Feb 2019 07:32:41 No.10407539 Report

Quoted By: >>10410038

>>10407413
>redpill me on limits
Please, take a seat...

Anonymous

Anonymous Fri 22 Feb 2019 09:07:08 No.10407677 Report

Quoted By:

>>10407413
The e-d definition says that, no matter the predefined accuracy you impose (any e>0), I can find an index (for series) or a value of the argument x (for functions) starting with which my "approximation" (which I call the limit) will be no further than e from any other value in your series.

Anonymous

Anonymous Fri 22 Feb 2019 09:16:56 No.10407691 Report

Quoted By: >>10407725

>>10407413
>It still feels like magic, or a cheat, though I don't believe it is.

That's honestly bizarre to me, as it's the one thing that feels properly rigorous and not 'cheating' to me.

Anonymous

Anonymous Fri 22 Feb 2019 09:44:16 No.10407725 Report

Quoted By:

>>10407691
What other things seemed like cheating to you?

Anonymous

Anonymous Fri 22 Feb 2019 19:57:34 No.10408838 Report

Quoted By: >>10408974

I guess what seems the most difficult at this point is proving a function has a domain over the reals. IDK I'll reread the chapter and do the exercises and see where I end up.

Anonymous

Anonymous Fri 22 Feb 2019 21:11:45 No.10408974 Report

Quoted By: >>10408998

>>10408838
>proving a function has a domain over the reals
You need a domain to define a function in the first place, so you just check if the domain is R from the definition of the function you want to check

Anonymous

Anonymous Fri 22 Feb 2019 21:24:26 No.10408998 Report

Quoted By: >>10409025 >>10409030

>>10408974
What can I read about to learn more about defining functions and determining their domains?

Anonymous

Anonymous Fri 22 Feb 2019 21:38:43 No.10409025 Report

Quoted By: >>10409894

>>10408998
You do not "determine the domain". When the function is defined, the domain is already part of the definition. Jeezus.

Anonymous

Anonymous Fri 22 Feb 2019 21:41:17 No.10409030 Report

Quoted By:

>>10408998
en.wikipedia.org/wiki/Function_(mathematics)

Anonymous

Anonymous Sat 23 Feb 2019 05:10:42 No.10409894 Report

Quoted By: >>10410028 >>10410634

>>10409025
That is pure circular reasoning that can be identified despite my ignorance on the subject. Not all functions have the same domain, so something about the function itself determines the domain or vice versa.

Anonymous

Anonymous Sat 23 Feb 2019 06:47:51 No.10410028 Report

Quoted By: >>10411414

>>10409894
Not circular, you've just got it twisted around: a function is, in very informal terms, a set of pairs of items between two given sets. Thus the domain and codomain, as well as the rules for assigning elements from the domain to the codomain through the function, define that function.

Anonymous

Anonymous Sat 23 Feb 2019 06:59:39 No.10410038 Report

Quoted By:

>>10407539
I was just thinking how I haven't seen this guy show up in a while.

Anonymous

Anonymous Sat 23 Feb 2019 15:20:11 No.10410634 Report

Quoted By: >>10411414

>>10409894
>That is pure circular reasoning
It's by definition, dumbass
>despite my ignorance on the subject
No

Anonymous

Anonymous Sat 23 Feb 2019 21:16:21 No.10411414 Report

Quoted By: >>10411426

>>10410028
Right, so my original question is still completely valid. What methods does one use to determine the domain of a given function?
>>10410634
retard. only reason you got me into a trap is because you were unable to answer my question so framed it as impossible. now when the result of your logic is carried out we end where we started. What methods does one use to determine the domain of a given function?

Anonymous

Anonymous Sat 23 Feb 2019 21:22:35 No.10411426 Report

Quoted By: >>10411450

>>10411414
>What methods does one use to determine the domain of a given function?
Let's say I want to determine the domain of some function f. Now, I cannot determine its domain unless I know what f is. So the definition of f must be given. In the definition of f, there is a domain, since a function by definition includes a domain, codomain, and a relation between the domain and the codomain. I look at the definition of f, usually will be something like "let f: R -> R be a function". I look at the part after the colon and before the arrow, that is the domain. I have now determined the domain of f.

Anonymous

Anonymous Sat 23 Feb 2019 21:36:16 No.10411450 Report

Quoted By: >>10411464

>>10411426
>How to find a function's domain
>Define or find the definition of f
>See what the domain is
>profit

This is the circular reasoning.
Just because you can define a domain for a function doesn't mean it can be computed for all values in that domain. Defining a domain that cannot be fully computed by the function implies a contradiction; surely you must be able to compute the full domain.

Anonymous

Anonymous Sat 23 Feb 2019 21:42:08 No.10411464 Report

Quoted By: >>10411520 >>10411534

>>10411450
If f(x) is undefined for some x in the domain, then f is not a function. But I said:
>Let's say I want to determine the domain of some function f.
Which means f is function. There is no circular reasoning, you're just illiterate.

Anonymous

Anonymous Sat 23 Feb 2019 21:58:39 No.10411514 Report

Quoted By:

Math is a mental trick that help us understand the universe, anon

Anonymous

Anonymous Sat 23 Feb 2019 22:01:32 No.10411520 Report

Quoted By: >>10411552

>>10411464
>If f(x) is undefined for some x in the domain, then f is not a function
That's not true.
>Let's say I want to determine the domain of some function f.
>Which means f is function.
Your logic here is literally, f(x) is a function it its domain is completely defined.
And its domain is completely defined as long as f is a function.

This is literally all you've been repeating, every response has had two stop circular logic.

Anonymous

Anonymous Sat 23 Feb 2019 22:06:20 No.10411534 Report

Quoted By: >>10411564

>>10411464
You might be technically correct, but you aren't answering the question in any meaningful way.

Anonymous

Anonymous Sat 23 Feb 2019 22:15:41 No.10411552 Report

Quoted By: >>10411582

>>10411520
>That's not true.
It is, by the definition of function.
>Your logic here is literally, f(x) is a function it its domain is completely defined.
f being a function implies f(x) is defined for all x in its domain, by the definition of function.
>And its domain is completely defined as long as f is a function.
I don't understand what you're trying to say here. Are you trying to say "f is a function implies it has a domain"?
>This is literally all you've been repeating, every response has had two stop circular logic.
I don't know what to tell you. It might seem like circular logic because you don't know the definition of a function, but it's definitely not.

Anonymous

Anonymous Sat 23 Feb 2019 22:20:12 No.10411564 Report

Quoted By:

>>10411534
It's not my fault the question is so dumb. How can I answer it in a meaningful way? It's like asking "how do I determine the binary operation of a group". You just look at the definition of the group and the binary operation will be there.

Anonymous

Anonymous Sat 23 Feb 2019 22:26:42 No.10411582 Report

Quoted By: >>10411585

>>10411552
f being a function implies f(x) is defined for all x in its domain, by the definition of function.

You miss the point. I'm no asking about exceptions in the domain, I am talking about the domain itself, and if it includes the real numbers. Obviously not every domain or set is defined for the real numbers, so its clearly an excellent question to ask what features of an operation define its domain.

Anonymous

Anonymous Sat 23 Feb 2019 22:29:28 No.10411585 Report

Quoted By: >>10411595

>>10411582
>I am talking about the domain itself, and if it includes the real numbers.
Check if f(x) is defined for all real x

Anonymous

Anonymous Sat 23 Feb 2019 22:33:16 No.10411595 Report

Quoted By:

>>10411585
Yeah dawg I'll check Wikipedia and if the operation isn't established I'll just pray to god to send me an answer.

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