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eegocentrik t1_j28qg64 wrote

Reply to comment by xSteee in There’s just as many numbers between 0 and 1 as there is from 0 to infinity. by Resinate1

Definition:

fraction, In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

The original number being expressed as a quotient. Fractions are quotients of the original number but not new numbers in themselves.

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xSteee t1_j28qy78 wrote

So 1/4, or 0.25, is not different from 3/4, or 0.75? Or are you saying that 0.25 and 0.75 are not numbers at all?

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eegocentrik t1_j28s8lc wrote

.25 and .75 are quotients of 1 and not independently new numbers.

1/4 == .25

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xSteee t1_j28sm8e wrote

Does it extends to number above 1? 2.25 and 2.75 are not different number?

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eegocentrik t1_j28u8wa wrote

Sure.

The .25 in 2.25 is the quotient of from 2 to 3 (1). 2+.25

Also, 2.25 is the quotient of 45 ÷ 2 or 45/2.

However, the OP said from 0 to 1, this is where my argument lies.

There are NOT the same amount of numbers from 0 to 1 as there are 0 to infinity.

There ARE the same number of ELEMENTS.

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xSteee t1_j28vjyh wrote

And the elements of a set of number ("all the numbers between 0 and 1" is a set of numbers, right?) are called...?

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eegocentrik t1_j28vo6x wrote

Quotients.

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xSteee t1_j28vv0o wrote

And a quotient, by definition, is "the number we obtain by dividing a number by another"

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eegocentrik t1_j28wc0a wrote

It's not a new number. It's a fractional representation of the numerator and does not exist outside of it.

There are not infinite NUMBERS between 0 and 1 only elements.

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xSteee t1_j28xebs wrote

Have you ever heard of real numbers? Irrational numbers?

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eegocentrik t1_j28xw3p wrote

Yes, irrational numbers do not apply here.

This is not a math issue, this is a semantic issue.

Fractions are quotients of rational numbers.

1 is the smallest unit of count.

Half of 1 can be represented by the quotients 1/2 or .5

Half of one can also be expressed as 2 new things that are not 1.

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xSteee t1_j290guf wrote

And we, as as species, for hundreds of years have decided to call them number too, so 0.5 is a number

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