Submitted by Resinate1 t3_zyzi9w in Showerthoughts
eegocentrik t1_j28ocaf 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
Define fraction.
xSteee t1_j28ou9b wrote
Fractions are another way to represent finite and infinite decimal numbers
eegocentrik t1_j28p4xp wrote
Not a definition.
Please define fraction.
xSteee t1_j28pjie wrote
A fraction is a numeral which represent a rational number. It is composed by a numerator and a denominator.
eegocentrik t1_j28qg64 wrote
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.
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?
eegocentrik t1_j28s8lc wrote
.25 and .75 are quotients of 1 and not independently new numbers.
1/4 == .25
xSteee t1_j28sm8e wrote
Does it extends to number above 1? 2.25 and 2.75 are not different number?
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.
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...?
eegocentrik t1_j28vo6x wrote
Quotients.
xSteee t1_j28vv0o wrote
And a quotient, by definition, is "the number we obtain by dividing a number by another"
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.
xSteee t1_j28xebs wrote
Have you ever heard of real numbers? Irrational numbers?
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.
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
Nilonik t1_j28p48j wrote
A fraction is a number which can be written as a/b, where a and b are integers, while b is unequal to zero.
eegocentrik t1_j28pvt0 wrote
And b. is the number, and a. is its fraction.
a. cannot be a unit of its own and does not exist without b. in this example.
Viewing a single comment thread. View all comments