Math Is Fun Forum

aleclarsen12

Member

Registered: 2008-06-01

Posts: 36

∞+½=½

This makes no sence...
∞+1/2=1/2

Did I do something wrong.. or is this right?

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: ∞+½=½

You've concluded that 1/2 = 1/2... which seems to be correct.  But why the first step:

∞+1/2=1/2

?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

iamthepro

Member

Registered: 2008-06-01

Posts: 1

Re: ∞+½=½

infinity is 1/0 not 0/1

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: ∞+½=½

You might like to read What is Infinity?: ∞+½=∞

And instead of 1/0 it is better to say

Which says that the "limit" of 1/x approaches ∞ as x approaches 0. In other words, we are not saying what happens when we *get to* 1/0, but about what happens as we get closer and closer. It may seem like a technical point, but it is important.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

iamthepro

Member

Registered: 2008-06-01

Posts: 1

Re: ∞+½=½

so what happens when x actually gets to 0 XD
(pardon my low leveled math =X)

Last edited by iamthepro (2008-06-01 23:27:53)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: ∞+½=½

When x gets to 0 the equation self-destructs, releasing massive amounts of energy ... so beware

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: ∞+½=½

When x gets to 0 the equation self-destructs, releasing massive amounts of energy ... so beware

For proof of this, see here: http://www.youtube.com/watch?v=CLxMN5YMS3A

iamthepro

Member

Registered: 2008-06-01

Posts: 1

Re: ∞+½=½

hahahaha that video is extremely hilarious

All_Is_Number

Member

Registered: 2006-07-10

Posts: 258

Re: ∞+½=½

You might like to read What is Infinity?: ∞+½=∞

And instead of 1/0 it is better to say

Which says that the "limit" of 1⁄x approaches ∞ as x approaches 0. In other words, we are not saying what happens when we *get to* 1/0, but about what happens as we get closer and closer. It may seem like a technical point, but it is important.

The limit of 1⁄x as x approaches 0 doesn't actually exist, since the answer is different depending on the direction from which x approaches 0.

We can say that the limit of 1/x approaches ∞ as x approaches 0 from the positive side, and that the limit of 1/x approaches -∞ as x approaches 0 from the negative side. We can also say that the "limit" of the absolute value of 1⁄x approaches ∞ as x approaches 0.

It's just a small detail, but an important one for those who are just learning the concept of limits.

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Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: ∞+½=½

http://www3.hi.is/~pjo1/division%20by%20zero.jpg

http://halshop.files.wordpress.com/2007/03/phpw9jvl0pm.jpg