When did you finally realize that limits are an ill-defined concept

Why?

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>2011
>gives a fuck about rigor

Shiggity diggity. Geniuses go with pure intuition.

>>9091997
When did you finally realize that mathematics is an ill-defined concept?

>>9091997
You ill-comprehending a concept does not make it ill-defined.

>>9091997
whats not to understand
lil arrow be sayin "move to the left realllly far" and the graph be like "o sshiiit duck!!" lmao

>>9092060
Kys

Well in high schools they are badly defined but delta/epsilon make them pretty rigorous.

They're not.

>>9092064
:(

>>9092067
How do you use delta epsilon with limits tending to infinity?

>science that isn't applied

>caring about mental masturbation while claiming to be empiricist

>>9091997
Looks like /mg/ is leaking.

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>>9091997
when limits are what people use to prove 1 = .999

>>9092001
He's a shitposter from the /math/ general. Report and ignore.

>>9092851
Replace one or both less-thans with greater-thans

>>9091997
Almost instantly. You pretty much have to be retarded not to.

>>9092876
>emp*ricist
So a retard in other words?

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>waiting for a single argument what is "ill" with the concept or definition of limits

>>9093009
>waiting for a single argument for why "limits" are well-defined

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>>9091997
This was all sorted out in the nineteenth century you retard

>>9093012
for any number there's some number such that some inequality implies other inequality. there's absolutely no unambiguity in a statement of this type.

>>9093024
What do you mean by "number"? What do you mean by "equality"?

>>9093012
Just go and do a course in analysis. All will be revealed.

Protip: Hard work required.

>>9093027
Analysis should be banned.

>>9093026
>What do you mean by "number"
an element of an ordered field
>What do you mean by "equality"
the diagonal relation on said field

>>9093030
>"ordered"
>"field"
>"relation"

>>9093030
>an element
What do you mean precisely by "an element"?
>an ordered field
Which ordered field? Can fields in general be shown to exist? If so, can they be shown to be well-defined?

>>9093030
he thinks equality is decidable for non natural numbers


HHHHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA

>>9093035
Equality on the so-called "real" numbers doesn't have to be decidable for you to use it in an implication.

>>9093027
Analysis relies heavily on ill-defined and non-existent garbage.

>>9093035
In classical logic everything is trivially decidable.

>>9093033
https://en.wikipedia.org/wiki/Main_Page
>>9093034
>Which ordered field
any
>Can fields in general be shown to exist? If so, can they be shown to be well-defined
yes and yes, not gonna do this, read a book

>>9093046
>any
You haven't shown that even a single one exists.

>>9091997
>limits are ill-defined
No, your understanding of limits is ill-defined.
Lrn2limits fgt pls

>>9093049
Why are these "limits" well-defined? Please explain.

>>9093053
>Please explain.
Do your own homework fgt pls.

>>9092887
1=0.9999.... because they are decimal expansions of the same thing. You don't need a limit to see that.

>>9093061
>1=0.9999.... because they are decimal expansions of the same thing
Prove it.

>>9093060
I see, so your understanding of "limits" is absent. That's not surprising since "limits" are merely an ill-defined fabrication.

>>9093062
1/1=1
1/1= 0+9/10+1/10=0.9+9/100+1/100 and so on.
qed

>>9093068
>and so on.
What is the formal meaning of this?
>qed
You can only use this after finishing a proof.

>>9093068
[eqn]1=0.9+0.1=\lim_{n\rightarrow\infty}{10^{-n}+\sum_{k=1}^n{9*10^{-k}}}=0.999...+0[/eqn]
I hope I didn't mess up any counters.

>>9093077
Now show that limits are well-defined.

>>9093080
It works well by not using limits and instead describing it meta-wise with symbol manipulation.
0.9+0.1=0.99+0.01=0.999+0.001 etc.
using purely such a description is perfectly valid.

>>9093081
>etc.
What is the precise formal meaning of this?

>>9093082
>etc.
it means continue inserting 9s and 0s and you wil see that the symbol chain at the front becomes 0.9999... and the other one becomes 0.000...0001, which if you go back to math equals 0.
At least realize, that we are talking about representations, so you can indeed work with them and their meaning, when doing this proof.

>>9093086
though I prefer the proof from 5th grade:
1/9=0.111...
2/9=0.222...
3/9..
...
8/9=0.888...
9/9=0.999...
9/9=1/1=1

>>9091997
Chapter XV of "An Introduction to Mathematics" by Whitehead, in which he actually defines them rigorously.

>>9093086
>0.9999...
What does the "..." mean?

I don't even remember.ber that basic shit. It would be f(x)=0 and lim1+/-=0 ?

>>9091997
When I realized that infinitesimals were clearly the way to go, and we should've abandoned the epsilon-delta approach decades ago.

>>9093091
>pattern continuation
Oh, nice proof method. Allow me to prove a theorem with it:
Theorem: 4<4
1<4
2<4
3<4
Ergo
4<4

QED

>>9093100
that a nrverending string of 9s is counted up in order to represent this number

>>9093157
only works for representations, not for calculations

>>9092851
Let {x_n} a sequence of reals. {x_n} approaches infinity iff for every N>n: |x_n|>M for every real number M.

>>9093474
>reals
No such thing.

>>9093491
ur a faggot read some axiomatic set theory, u can define reals as an equivalence class of the integers or with Dedekind cuts

>>9093497
>axiomatic set theory,
Which one of them? Any theory which defines the so-called "real" numbers is inconsistent.

>>9093513
yeah ZFC axiomatic set theory is the way to go, Godel's incompleteness theorem included

>>9093517
ZFC is complete garbage.

>>9093532
fuck u nihilistic fuck

>>9093513

You're just grasping at straws and trying to jerk yourself off by using completely impossible standards of rigor. People like you remind me of those idiots who demand that one proves to their satisfaction that 1+1=2.

It's all just sophistry. In the real world the working definition of what a "limit" is has been well established for over a hundred years and when you're trying to send a rover to Mars, thats the definition you'll be using for your calculation. Anything else is just pseudo-intellectuals busy bodies trying to make themselves feel important.

[math]\frac{1}{\infty}=0[/math]

There is literally nothing wrong with this.

>infinity is not a number, in [math]y=\frac{1}{x}[/math], as x nears infinity, y approaches but never equals 0

If it is not a number, as you say, then it is fine to not to treat it like a number. Only brainlets can't think outside the box.

[math]\frac{1}{\infty}=0[/math], yes, everything you have been taught and the world's finest minds are wrong, why they did not reach this conclusion before I did, I don't know. but they are, as I have just provn, end of discussion

>>9093547
"limits" fundamentally don't make any sense. They can't be "well-defined". You can use any made up bullshit you like, just don't lie about it.

>>9093549
ε-δ mate.

>>9093553
"real numbers" fundamentally don't make any sense. They can't be "well-defined". You can use any made up bullshit you like, just don't lie about it.

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>>9093549

Limits are just a mathematical "tool" that we use. You say they're abstract, but so is calculus and a host of other things that can be hard to "rigorously" (by whatever made up standard you employ) define but are used every single day by all scientific disciplines to achieve tangible demonstrable results.

Again, if we used your standards consistently, mathematics would have never evolved and we would all be crazy solipsists writing 100 page peer reviewed papers trying to prove that one plus one equals two.

Let me get back to the fundamental issue that I alluded to in my previous post: If you were put in charge of sending a rover to Mars, would you use limits in your calculations or not? If the answer is that you would use them, then you're just being a sophist and this entire discussion is just you trying to suck your own cock

>Muh axiomatic tower

This whole thread is why mathematicians are obselete and irrelevant

>>9093567
>crazy solipsists writing 100 page peer reviewed papers trying to prove that one plus one equals two.
>implying that's not what mathematics is becoming

>>9093629
t. utter fool

>>9093165
That's pretty retarded, bruv.

>>9092060
>>/reddit/

>>9093548
See this is wrong though.

1/infinity != 0

limits are ill-defined

When ever you evaluate a non-trivial limit, you inevitably get to a point where you have to rely on "hurr durrr well it loookss like it approaches this number"

>>9091997
>When did you finally realize that limits are an ill-defined concept in mathematics?
but they are not. the contrary is true. Cauchy came up with it to make mathematics rigorous.

>>9093767
>When ever you evaluate a non-trivial limit, you inevitably get to a point where you have to rely on "hurr durrr well it loookss like it approaches this number"
no. you have to rely on non brainlets to break it down to obvious limits.

>>9093728
>1/infinity != 0
>limits are ill-defined
ahahahaha i FUCKING knew it.
you have not understood what a limit actually means.

you probably think lim_x->0 1/x = infinity means 1/0 = infinity

LEL

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this >>9092002

we are all engineers

>>9093785
No you brainlet...

1/infinity != 0

the limit of 1/n as n -> infinity = 0

There is a huge difference between these two statements, and if you don't understand that, you are in fact a brainlet.

>>9091997
define "ill-defined"