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

Topics that don't fit anywhere else.
Tennise
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### sets: definition of "fraction" raises ambiguity regarding Q

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 $\mathbb{Q}$?
All integers can be placed in a fraction, $2\over1$. $\mathbb{Z} = \mathbb{Q}$?
Decimals can convert to fractions, are they defined by $\mathbb{Q}$? 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.

stapel_eliz
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I think the definition of a 'fraction' raises some ambiguity: what is a fraction in terms of what can be defined by $\mathbb{Q}$?
Any value which can be expressed as a ratio of integers will belong in $\mathbb{Q}$.
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...

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

http://www.purplemath.com/modules/setnotn.htm
...
Decimals can convert to fractions, are they defined by $\mathbb{Q}$? ....
Some decimals can be written as a fraction of integers.

Tennise
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### Re:

Any value which can be expressed as a ratio of integers will belong in $\mathbb{Q}$.
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 $\mathbb{Q}$?

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)...

stapel_eliz
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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

I see, thanks!

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

stapel_eliz
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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....)