Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2014-10-29 03:34:26
Formal Limits
Consider f(x) = x+3
How do I show that f(x) does not tend to 3 as x tends to 0, formally?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#2 2014-10-29 04:12:06
- Olinguito
- Member
- Registered: 2014-08-12
- Posts: 649
Re: Formal Limits
Bassaricyon neblina
Offline
#3 2014-10-29 05:24:00
Re: Formal Limits
I've tried that, what do you do about del?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#4 2014-10-29 09:12:50
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Formal Limits
How can you show something that is not correct?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Offline
#5 2014-10-29 11:12:05
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Formal Limits
You do have a point.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#6 2014-10-29 20:22:35
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Formal Limits
Thanks Stefy. 
I thought I was just being stupid.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#7 2014-10-29 21:08:08
Re: Formal Limits
Sorry guys 
Let f(x) = x+3
How do I show that f(x) does not tend to 0 as x tends to 0, formally?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#8 2014-10-30 01:42:47
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Formal Limits
Oh 
You have to show that in a small neighbourhood of x = 0, f(x) is not in a small neighbourhood of zero. As f(0) = 3, that shouldn't be hard.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#9 2014-10-30 02:03:06
Re: Formal Limits
f(x) is not in a small neighbourhood of zero
What is a neighbourhood?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#10 2014-10-30 02:13:11
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Formal Limits
If e is small then x +/-e is a neighbourhood of x.
And f(x +/-e) is the corresponding neighbourhood of f(x).
Let's take +e. -e is similar.
Then f(0 + e) = 0 + e + 3
No matter how small e gets, e + 3 is not close to 0.
http://en.wikipedia.org/wiki/Limit_(mathematics)
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#11 2014-10-30 02:17:49
Re: Formal Limits
But, I can make e big enough to make e+3 close to 0
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#12 2014-10-30 03:34:27
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: Formal Limits
First you choose an e so that your x point is close to zero. Then you generate f(0+e) . If it's close to zero, then choose a smaller e. The limit rule requires that you can get arbitrarily close. Something like this:
x e f(x+e)
0 -3 0 (oh dear I seem to have reached zero, but now to reduce e ..)
0 -2 1
0 -1 2
0 -0.5 2.5
0 -0.25 2.75
0 -0.1 2.9
0 -0.01 2.99
etc
As e gets smaller and I get closer to x = 0, f(x) does not get closer to zero. (It gets closer to 3 of course.)
So you might be able to choose an e that makes f(x) = 0, but that's not enough. You have to show that as the x gets closer to zero, the f(x) gets closer to whatever.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#13 2014-10-30 05:51:16
Re: Formal Limits
Oh, thanks!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
Pages: 1