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April 14th, 2017, 05:56 PM   #1
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0/0 Indeterminate or undefined?

I was reading something earlier today on Quora where someone said that 0/0 is not equal to indeterminate. Are they right?
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April 14th, 2017, 06:04 PM   #2
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A limit may be indeterminate. A function is either defined or undefined over an interval(s).

... 0/0 depends on context.
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April 14th, 2017, 06:18 PM   #3
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ahh ok, I think I'm getting it now. I've always thought there was big difference between 0/0 and non-zero/0. The former could have an infinite number of results whereas the latter there is no result.
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April 14th, 2017, 07:49 PM   #4
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I would prefer to say that, speaking informally, non-zero over zero never has a finite result and that zero over zero sometimes has a finite result that can be determined with additional information.

The above formulation is not strictly correct, but it explains the difference in usage between "undefined" and "indeterminate."

Under standard analysis of the real numbers, anything over zero is undefined (meaning not a real number); the limit of non-zero over zero is never a real number, but in some cases the limit of zero over zero is a real number. In analysis, there is a big difference between the value of a function at a point and the value of its limit at a point.
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Last edited by JeffM1; April 14th, 2017 at 07:52 PM.
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April 15th, 2017, 05:07 AM   #5
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This is the question below I was reading:

https://www.quora.com/Is-indetermina...with-undefined

And in the back a forth this slideshare paper is mentioned:

https://www.slideshare.net/MrInderer...with-undefined

Like, it makes a case for something that I've thought for years to be the case. Now, I'm not going to drink the cool aid and say I support the conclusion, but yea its pretty compelling to me.

What do I need to read up on to get why this conclusion is wrong?
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April 15th, 2017, 05:24 AM   #6
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That slideshare is nonsense. Only the title is accurate. There are some accurate ideas behind what appears in the slides, but they have been mangled into inaccuracy. Whether this is because the author doesn't understand or whether it is because the are trying to oversimplify the ideas is hard to say.

You need to understand the theory of limits for "indeterminate" to make sense.

Not that nothing is "equal to indeterminate" nor is anything "equal to undefined". It's like saying that "Everest is equal to tall".

As a rule of thumb, anyone that turns to a dictionary definition in writing about mathematics doesn't understand mathematics. Mathematics provides its own, technical definitions of words. They have a specific meaning in a specific context.
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April 15th, 2017, 04:07 PM   #7
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Yea, Merriam Webster was clearly a poor reference choice on the part of the author. However, after looking at the Wolfram definitions:
1. a numerical quantity whose magnitude cannot be determine.
2. returned when a value cannot be unambiguously defined.

Indeterminate—Wolfram Language Documentation

It appears the authors assertion that the lack of a unique answer for 0/0 as being the reason for the indeterminate label is a correct one. Though maybe Wolfram is wrong too!! What reference should I look at?
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April 16th, 2017, 06:14 AM   #8
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Wolfram is probably reliable, although the title looks like a language reference link rather than a mathematical dictionary. Your definitions will come in the text you use to study. Wikipedia is usually reliable too.

I didn't say that the author's definition wasn't more or less accurate for the word. Most mathematical definitions do bear some resemblance to the natural language definition for obvious reasons.

But you wouldn't trust definitions of English words taken from a Spanish dictionary, so why trust definitions of Mathematical words from an English dictionary?
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April 17th, 2017, 12:40 PM   #9
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Here is a nice quote on the subject.

Quote:
Professor C Inglis : Applied Mechanics for Engineers

Having to evaluate an expression of the form 0/0 is the penalty you have to pay for over-idealization and is an indication that the treatment of the problem is at variance with nature

Last edited by studiot; April 17th, 2017 at 12:44 PM.
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April 17th, 2017, 01:01 PM   #10
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I would suggest that the fact that one is doing mathematics is an indication that the problem is at variance with nature. It doesn't necessarily stop your model from being good enough though.
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