What is a fraction? (By definition)

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FrOzeN

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Nov 8, 2006
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I'm trying to assert the most exact definition of a fraction, based on a strictly Mathematical point of view.

http://mathworld.wolfram.com/Fraction.html

http://dictionary.reference.com/browse/fraction
1. Mathematics.
a. a number usually expressed in the form a/b.
b. a ratio of algebraic quantities similarly expressed.
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Would the two following examples be considered fractions? If both yes and no, then could you define which is the technical reasoning, and which is the more colloquial definition.

\(\displaystyle sqrt{2} \over 1\) and \(\displaystyle \pi \over 4\)

Also, what about the following:

\(\displaystyle Circumference \over Diameter\)

I'm asking you guys this as there seems to be a stupid debate about it over on another forum, and I'm curious to see the perspective of those who are likely highly qualified in Maths. Thanks.
 
There may be come confusion about the difference between "fraction" and "rational number".

There may be some confusion about the difference between a number and an expression representing a number.

Does "fraction" NEED to be well-defined? If "fraction" has no formal, sound, bullet-proof, rigorous definition, will all of mathematics suddenly explode?

Must the definition be restricted to mathematics? (Fred/Dog) looks pretty much like a fraction to me.

Sounds to me like a discussion not worth much time.

There is one important social misuse of the word "fraction". It appears often in local advertising announcing a really big sale. The phrase most often used is, "...at a fraction of the cost..." This assumes 0 < fraction < 1, which is a little silly, since there is no such formal definition. Wouldn't the consumer be shocked to see the new price at (5/3) of the original price?! Some sale... Wouldn't the seller be disturbed to be forced to sell at (-1/10) of the original price. They're paying us to take stuff!
 
I'm asking you guys this as there seems to be a stupid debate about it over on another forum,
Click to expand...

I've seen many a geeky discussion on some of the forums. I shouldn't wonder.
 
Jethro Bodine s'got it down pat: geezintos

Jethro: 2 geezinto 4 2 times...
Jed: Hear that Granny? That boy's sure to graduate to grade 3 !
 
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