sets: definition of "fraction" raises ambiguity regarding Q

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Tennise
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sets: definition of "fraction" raises ambiguity regarding Q

Postby Tennise » Sat Jun 06, 2009 6:44 pm

http://www.purplemath.com/modules/setnotn.htm
I think the definition of a 'fraction' raises some ambiguity: what is a fraction in terms of what can be defined by ?
All integers can be placed in a fraction, . ?
Decimals can convert to fractions, are they defined by ? And does this apply to both terminating and recurring decimals or just terminating?

I've never come across set terminology in class so I'm curious to know when the average school would use these.

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stapel_eliz
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Postby stapel_eliz » Sat Jun 06, 2009 8:05 pm

Tennise wrote:I think the definition of a 'fraction' raises some ambiguity: what is a fraction in terms of what can be defined by ?

Any value which can be expressed as a ratio of integers will belong in .

Tennise wrote:I've never come across set terminology in class so I'm curious to know when the average school would use these.

That's a whole different issue... :shock:

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Martingale
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Re: sets: definition of "fraction" raises ambiguity regarding Q

Postby Martingale » Sat Jun 06, 2009 8:54 pm

Tennise wrote:http://www.purplemath.com/modules/setnotn.htm
...
Decimals can convert to fractions, are they defined by ? ....


Some decimals can be written as a fraction of integers.

Tennise
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Re:

Postby Tennise » Sat Jun 06, 2009 9:11 pm

Thanks for your responses,
stapel_eliz wrote:Any value which can be expressed as a ratio of integers will belong in .


This clarifies it for the most part, just one thing: recurring non-repeating decimals can't accurately be placed in a fraction, would these be exceptions or would they be included in ?

I understand that the school system varies a lot, I just hope that upcoming tests review what has been covered in class, this of which has not (as far as I know, the tests are not prepared internally and we probably will stumble across these prior to learning them)...

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stapel_eliz
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Postby stapel_eliz » Sat Jun 06, 2009 10:06 pm

No, irrational numbers (which are non-repeating, non-terminating decimals) can not be included within the set of rational numbers.

Tennise
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Re: sets: definition of "fraction" raises ambiguity regarding Q

Postby Tennise » Sat Jun 06, 2009 10:15 pm

I see, thanks!

hmm, I saw a button on here to mark the thread as "solved" before but it seems to have disappeared...

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stapel_eliz
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Postby stapel_eliz » Sun Jun 07, 2009 12:21 am

Tennise wrote:I see, thanks!

hmm, I saw a button on here to mark the thread as "solved" before but it seems to have disappeared...

The button should be back now. (A recent update messed up one lousy line of code....)

:wink:


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