My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news


Thanks Tree1Thanks
Reply
 
LinkBack Thread Tools Display Modes
September 16th, 2015, 04:52 AM   #11
Senior Member
 
Joined: Jun 2015
From: England

Posts: 915
Thanks: 271

Quote:
If it's "indeterminate", it's undefined.
If they are both defined to be the same, how do you determine which one to use?

What is your view on this question

x + y = 15. (x, y in R)

Determine x, y?
studiot is offline  
 
September 16th, 2015, 05:06 AM   #12
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,681
Thanks: 2659

Math Focus: Mainly analysis and algebra
They aren't the same. Indeterminate is a subset of undefined. Indeterminate only makes sense in the context of limits. In asking the value of $0 \over 0$, the OP is talking about a numerical operation which is undefined (because it involves division by zero). However, it is a ratio to which we can sometimes meaningfully assign a value based on the context. Because the value differs with the context, that value is indeterminate.
v8archie is offline  
September 16th, 2015, 08:36 AM   #13
Senior Member
 
Joined: Jun 2015
From: England

Posts: 915
Thanks: 271

Quote:
Because the value differs with the context, that value is indeterminate.
Yes I agree, that iswhat we have already said.

But context in a mathematical sense is more information, boundary conditions, equations whatever.

So consider my previous example

x + y =15 (x,y in R)

Find x and y

Both x and y are clearly defined, but they are undetermined or indeterminate; there are an infinite numebr of possible pairs of x and y that fit the information and definition supplied.

But if I also add x =10 or x = 2y or in the 0/0 format x/y = 2

Then x and y can be determined uniquely.

But they are never undefined.

Let us look further at the expression 0/0

consider Expression = E = {(x-3) *(x+5)} / (x-3), when x = 3.

This leads to E = (0/0) * (3+5) = (0/0) * 8

In this instance many define 0/0 as = 1 so E = 8

But this situation does not work with (8*3) / 0.

The problem is the division by 0, not the ratio of 0 to 0.

That is because, unlike 0/0, X/0 leads to a result that is not in R

Its difficult here because if I use mathml on the other computer I can't see the result.
and I can't use it here.

Last edited by studiot; September 16th, 2015 at 08:38 AM.
studiot is offline  
September 16th, 2015, 09:07 AM   #14
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,681
Thanks: 2659

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by studiot View Post
In this instance many define 0/0 as = 1 so E = 8
I've never seen anyone do that, and they'd be wrong if they did. The function you give is undefined at $x=3$. But it's a removable discontinuity which simply means that the two-sided limit as $x \to 3$ exists and is finite.

The only reason you get ${0 \over 0} = 1$ in there is because away from $x=3$ you have ${x -3 \over x-3} = 1$.

Last edited by skipjack; September 16th, 2015 at 03:44 PM.
v8archie is offline  
September 16th, 2015, 09:25 AM   #15
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,681
Thanks: 2659

Math Focus: Mainly analysis and algebra
$x+y=15$ defines an infinite number of ordered pairs $(x,y)$. In the $x,y$-plane the pairs are points on a line.
v8archie is offline  
September 16th, 2015, 10:18 AM   #16
Senior Member
 
Joined: Jun 2015
From: England

Posts: 915
Thanks: 271

The fact remains that there is no additional information you can supply that will lead to a result (in R) of division by zero (because it is not defined)

This is different from 0/0 where additional information can lead to a result.

This is why define and determine are different words, not subsets of one or the other.
studiot is offline  
September 16th, 2015, 02:12 PM   #17
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,681
Thanks: 2659

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by studiot View Post
not subsets of one or the other.
I agree with everything else you wrote apart from the above.
v8archie is offline  
September 16th, 2015, 07:45 PM   #18
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Quote:
Originally Posted by ABRAR View Post
?
ABRAR, who are you and why are you lurking around
like a spook at Halloween?
Denis is offline  
Reply

  My Math Forum > Math Forums > Math

Tags
mind boggling, weird



Thread Tools
Display Modes






Copyright © 2019 My Math Forum. All rights reserved.