Submitted by Resinate1 t3_zyzi9w in Showerthoughts
xSteee t1_j28nh6u wrote
Reply to comment by eegocentrik in There’s just as many numbers between 0 and 1 as there is from 0 to infinity. by Resinate1
0.1 is 1/10, a portion out of 10 of 1. 0.2 is 2/10, two portion out of 10 of 1. 0.1 and 0.2 are two different number.
Or am I misinterpreting something?
eegocentrik t1_j28nwgv wrote
A piece cut into ten pieces.
.1 is one PIECE of the original pie, not an entirely new pie.m.1 describes the piece, not the pie.
You could have .9 grams of the .1 piece, still not a new pie. There are no new numbers created by dividing the unit.
xSteee t1_j28o5od wrote
As someone said, numbers are not pies. It's like you are trying to demolish hundreds of years of maths by saying that fractions are not different numbers ahah
eegocentrik t1_j28ocaf wrote
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.
lt_Matthew t1_j28omf9 wrote
So if someone says they're eating pie, you correct them and say it's 'a piece of pie'?
eegocentrik t1_j28phh8 wrote
Only if they are counting it while they eat it.
Do you say that you plated 8 pies for dessert?
Or are there 8 pieces of pie on the counter?
Viewing a single comment thread. View all comments