sets: definition of "fraction" raises ambiguity regarding Q

Topics that don't fit anywhere else.
Tennise
Posts: 7
Joined: Sat Jun 06, 2009 7:12 am
Contact:

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
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
Tennise wrote: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 $\mathbb{Q}$.

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...

Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

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

Tennise wrote: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
Posts: 7
Joined: Sat Jun 06, 2009 7:12 am
Contact:

Re:

stapel_eliz wrote: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
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
No, irrational numbers (which are non-repeating, non-terminating decimals) can not be included within the set of rational numbers.

Tennise
Posts: 7
Joined: Sat Jun 06, 2009 7:12 am
Contact:

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
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
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....)