limit to positive infinity of x minus x

[babipsylon]

lim (x-x) for x going to infinity equals? Is it simply 1?

r

[Sensei]

Isn't x-x equal to 0?

And lim(0) you're interested to calculate.. ?

 

Do you meant?

[math]\lim_{x \to +\infty}f(x)=x-x[/math]

Edited July 28, 2016 by Sensei

[Country Boy]

In just a little more detail, for any finite x, x- x= 0 so [math]\lim_{x\to\infty} (x- x)= \lim_{x\to\infty} 0= 0[/math] not 1.

 

Perhaps you were thinking of [math]\lim_{x\to\infty} \frac{x}{x}= 1[/math] since [math]\frac{x}{x}= 1[/math] for any finite x.

Edited August 19, 2016 by Country Boy

[blue89]

if it has been asked this one

 

lim Xn = infinity

lim Yn = - infinity

 

lim (Xn + Yn) = 0 ??

 

yes ,this is right!

 

Edited August 27, 2016 by blue89

[Country Boy]

I strongly recommend that you learn a little Calculus before you criticize posts about Calculus. There is absolutely nothing in the original posts that suggest it is talking about sequences ​nor has anyone "written supposing so. The first post asks about the limit, as x goes to infinity of the function f(x)= x- x= 0 for all x and that is how it was answered.

 

(You might also want to learn something about both "science" and "religion" before you suggest that science is a religion. Many scientists would take exception to that.)

Edited August 27, 2016 by Country Boy

[blue89]

I am functional analysist and I think I am expert of basic analysis (I am mathematician BSc : Mathematics (istanbul university 2013) MSc sdu-mathematics , 2014 )

 

Basic Limit Form

 

for sequences

 

if n → ∞ An → a , then this will basically mean that

for any ε >0 and n ∈ N , for any Nε > n , │An - a │ < ε

This means ,the limit is a one point that almost all of other points are in neighborhood of the limit point

 

Some very shortTopological approach or contexts.

 

The limit point is important point why this point is being assessed at topology widely (especially in general and beginning descriptions )

for instance

when our An 's elemnts be elemnt of A¯ and An → a ,then this will be enough for us to say that the A set will be complete or will provide to reach such contexts.

however if An's elements were alement of A° we would not be able to say the same thing.

the compactness is also one of very important and we are able to ensure the compactness definition with almost the same similarity via using some sequences' properties (cauchy sequences - check also please bolzano - weierstrass theory - and "compactness" according to sequence approach)

Edited August 27, 2016 by blue89

[John Cuthber]

parrdon!

 

I am functional analysist and I think I am expert of basic analysis (I am mathematician BSc : Mathematics (istanbul university 2013) MSc sdu-mathematics , 2014 )

And yet you are still wrong.

[blue89]

And yet you are still wrong.

 

could you provide me please an evidence?

!!

[John Cuthber]

could you provide me please an evidence?

!!

It's difficult for me to supply evidence.

 

You made a claim that the first two replies in this thread referred to sequences.

There is nothing in the two posts that suggests that (it seems to me that they refer to x being a variable).

 

So, what evidence could I cite?

I could quote your post back at you to show that you wrote it if you feel that would help.

 

Also, re. "!!"

http://wiki.lspace.org/mediawiki/Multiple_exclamation_marks

Edited August 27, 2016 by John Cuthber

[blue89]

 

It's difficult for me to supply evidence.

 

 

 

ok. no problem.

 

Edited August 27, 2016 by blue89

[John Cuthber]

I'm well aware that you think you know what you are talking about.
I'm also aware that you made a claim but have not supported it in any way.

 

Perhaps, before you go, you should explain what it is in the first two replies that indicates that they suppose that they are referring to a sequence.

 

You seem to have forgotten that you said

"all of written mathematical expressions are INCORRECT in this thread. because x is not a sequence but all members have written supposing so."

[ajb]

Anyway... the problem here is that one should avoid trying to think of [math]\infty - \infty = \: ?[/math] Remember that infinity is not a real number and so one has to be very careful here and try to make sense of such thing using limits. Well, for the case at hand there is no real trouble as others have pointed out, x-x =0 and the limit of this as x gets large is clearly zero.

[blue89]

Anyway... the problem here is that one should avoid trying to think of [math]\infty - \infty = \: ?[/math] Remember that infinity is not a real number and so one has to be very careful here and try to make sense of such thing using limits. Well, for the case at hand there is no real trouble as others have pointed out, x-x =0 and the limit of this as x gets large is clearly zero.

 

 

I am afraid the first one must be incorect

 

1) An = n and n → ∞ , lim An = ∞

 

2) Bn = - n n → ∞ , lim Bn = - ∞

 

3) n → ∞ lim (An + Bn) = lim ( - n + n ) = lim (0) = 0

[ajb]

Yes, 3 is correct - in that n-n =0 and so this limit is 0 - and what others said very early on in this thread.

[blue89]

but of course this may not be correct everytime.

 

for instance if we prefer An = 2n ,Bn = - n

 

n → ∞ lim (An + Bn) would be lim (2n - n) = lim (n) = ∞

 

furthermore ,we use the ∞ and - ∞ point each as a one point in real analysis (but of course this is higher level (measure theorie commenecement descrptions)

Yes, 3 is correct - in that n-n =0 and so this limit is 0 - and what others said very early on in this thread. +++ ajb's initial comment

 

however ,that is true ,we may not approach as a normal point to these defimitions infinity and - infinity.

or this will affect many many thing.

for instance if we have any sequence which is has sphere , then we will be able to say this will have atleast one subsequence that it has limit although the real/main sequence is not cıonvergent (bolzano weierstrass theorem)

 

like this

 

if for any n ,there exist at least one M value and M > 0 ,if

I An I < M

 

then ,even if An is not convergent (has no limit ,because all convergent sequences should be sphered) ,An will have at least one subsequence like Ank

and Ank convergent

 

(bolzano weierstrass)

 

I mean that descriptions are important ok. if

 

n → ∞, lim (An) = ∞ or - ∞ ,then this would not ensure bolzano weierstrass theorem.

Edited August 28, 2016 by blue89

[ajb]

You are trying to over think this problem...

 

The function in question is just f(x) = x-x =0 which is defined on the real line. We then want to take the limit as x -> \infty, but as f(x) = constant this limit is just that constant, i.e. zero.

 

What one has to be more careful with is lim(x) - lim(x) = ? as x -> \infty. This is my point and I think what has confused people.

[blue89]

FUNCTIONAL APPROACH

 

we may say that if we would like to interprete any sequnce which is convergent,we will be able to say almost all of element of that sequence will be near the limit (just means at neighborhood of limit point) remember my first limit fom.

 

WHAT ABOUT FUNCTIONS ?

 

it is not the same of course ,but the technique is almost similar.

anfd furthermore ,topolgic approach would be very important ..

and I think might make more easy to understand because

at mathematics discipline generally all subjects have relationships and level to level ,for instance calculus is lower level than Real or Complex analysis

even if this will not mean as in actual form that ,if someone do not know calculus well ,he/she will not understand Real / complex analysis .

I am sure this will be very very difficult.

[ajb]

So, what is [math]\infty - \infty [/math]?

[blue89]

You are trying to over think this problem...

 

The function in question is just f(x) = x-x =0 which is defined on the real line. We then want to take the limit as x -> \infty, but as f(x) = constant this limit is just that constant, i.e. zero.

 

What one has to be more careful with is lim(x) - lim(x) = ? as x -> \infty. This is my point and I think what has confused people.

 

 

surprisingly I realised ! and must apologise!

 

at first I had thought x just as a point (because I could not see f(x) = x completely. so thought like x=a

 

...

about your expression , probably that one you writen must be also true. as I remember ,but I should check it.

 

I mean if f(x)= x ,and g(x) = - x , x → ∞ lim( f(x) + g(x)) = 0 (hımm continuoum would be required (don2t remeber well ,I must check it)

 

but the interval is also important.

So, what is [math]\infty - \infty [/math]?

 

I could not understand this question really.could you provie more information

 

...

when we study on functions

 

these are not the same things

x → ∞ and x → c (c is a real value or any value on the domain interval)

San-de -Wich theorem will be also effective there

So, what is [math]\infty - \infty [/math]?

 

this may define many many things...

Edited August 28, 2016 by blue89

[Country Boy]

I would say, rather, that [math]\infty- \infty[/math] does not define anything! You can have different limits, as the variable goes to infinity, that, if you just replace the variable with infinity would look like '[math]\infty- \infty[/math]'. But that does not mean that [math]\infty- \infty[/math] "defines" them. Rather, "subtraction" is not defined for "infinity" and, in particular, [math]\infty- \infty[/math] is not defined- it simply has no meaning!

Edited August 28, 2016 by Country Boy

[blue89]

I would say, rather, that [tex]\infty- \infty[tex] does not define anything! You can have different limits, as the variable goes to infinity, that, if you just replace the variable with infinity would look like '[math]\infty- \infty[/math]'. But that does not mean that $\infty- \infty$ "defines" them. Rather, "subtraction" is not defined for "infinity" and, in particular, $\infty- \infty$ is not defined- it simply has no meaning!

 

sure!

 

just because of this I wrote so detailed although it was so simple like this

 

lim ( x ) + lim ( - x) = lim (x - x) = lim (0) = 0

 

I remember when we were at first class ,someones were failing about such things ,for instance some of them were writing

 

f(x) = x , g(x) = - x , x → ∞ lim f(x) + g(x) = 0 (incorrect ,failed!) they should write

 

lm (f(x) + g(x)) = lim (x - x) = lim (0) = 0.

 

furthermore ,this is generally not enough ,Limit form is required (for functions )

 

general form

 

f(x) = 1/x , x = 1 x → 1 ,lim f(x) ?

 

any ε >0 , I x-1 I < δ , I f(x) -f(1) I < ε

 

controlling --->

 

f(x) = 1/x ,f(1) = 1

 

I f(x) - f(1) I = I 1/x - 1 I = I (1-x ) / x I ( I 1 - x I = I x - 1 I )

 

if we prefer ε = δ / ( F(δ ) ( δ > 0 )

 

,then this will be rigt that lim f(x) = 1 when x → 1

just the similarity which I implied between sequence and functions ,was between δ and ε (functional approach,limit )

 

and N and a (sequenceilimit)ü

 

Dear Hallsoflvy

thanks very much for your private message.

 

and your words was right ,about my remarks ...and I am going to rewrite to confirm your implication.

 

Kind Regards

 

NOTE PLASE ,I DID WRITE RELATION BETWEEN δ AND ε incorrectly at first ,this would be a bit different and so I wrote as F(δ)

if anyone would me to find what F was ,I will find/write it.

Edited August 28, 2016 by blue89

[Country Boy]

 

sure!

 

just because of this I wrote so detailed although it was so simple like this

 

lim ( x ) + lim ( - x) = lim (x - x) = lim (0) = 0

No, it is not. [tex]\lim_{x\to\infty} x+ \lim_{x\to\infty}(-x)[/tex] does not exist! [tex]\lim_{x\to\infty} (x- x)= \lim_{x\to\infty} (0)= 0[/tex].

 

I remember when we were at first class ,someones were failing about such things ,for instance some of them were writing

 

f(x) = x , g(x) = - x , x → ∞ lim f(x) + g(x) = 0 (incorrect ,failed!)

Which is what you wrote, above, which I said was incorrect.

 

they should write

 

lm (f(x) + g(x)) = lim (x - x) = lim (0) = 0.

 

furthermore ,this is generally not enough ,Limit form is required (for functions )

 

general form

 

f(x) = 1/x , x = 1 x → 1 ,lim f(x) ?

 

any ε >0 , I x-1 I < δ , I f(x) -f(1) I < ε

 

controlling --->

 

f(x) = 1/x ,f(1) = 1

 

I f(x) - f(1) I = I 1/x - 1 I = I (1-x ) / x I ( I 1 - x I = I x - 1 I )

 

if we prefer ε = δ / ( F(δ ) ( δ > 0 )

 

,then this will be rigt that lim f(x) = 1 when x → 1

just the similarity which I implied between sequence and functions ,was between δ and ε (functional approach,limit )

 

and N and a (sequenceilimit)ü

 

Dear Hallsoflvy

thanks very much for your private message.

 

and your words was right ,about my remarks ...and I am going to rewrite to confirm your implication.

 

Kind Regards

 

NOTE PLASE ,I DID WRITE RELATION BETWEEN δ AND ε incorrectly at first ,this would be a bit different and so I wrote as F(δ)

if anyone would me to find what F was ,I will find/write it.

[rahul_26]

If you want to study more about limit then this will help you-

http://www.actucation.com/calculus-1/limits-and-continuity/limits