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.

You do have me here.

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Please provide to me a source explaining that fraction are new individual numbers separate from their whole.

Pies are constructed

A fraction is a numeral which represent a rational number. It is composed by a numerator and a denominator.

Okay so 99.9989% I'm going to assume nobody saw Andrew Tate's box of pizza and hopped on the next available flight to Romania

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?

Pies are pies my friend. You were so close. Do you have a math teacher who can explain this? Or Google?

Pies are constructs.

Not a definition.

Please define fraction.

A fraction is a number which can be written as a/b, where a and b are integers, while b is unequal to zero.

Fractions are another way to represent finite and infinite decimal numbers

You say useful, I say keeps it keeps me up all night every night.

Also, do you just think of the words or do you actually hear yourself saying them in your head?

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Lol. Exactly!

Numbers are a construct and now you’re trying to define them in some real world way like pies. Thanks for helping me prove my point while trying to prove yours I guess.

If you keep wanting to disagree I obviously won’t mind since you’re actually just agreeing but feel free to look up this very established and agreed on mathematical concept that is again... agreed on by humans... the people that constructed it. As you so helpfully pointed out.

So if someone says they're eating pie, you correct them and say it's 'a piece of pie'?

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Define fraction.

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

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Numbers are constructs and don't really exist, and yes it does.

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.

Yeah I should’ve said 1 to infinity! Title typo

If I remember correctly, it has to do with rational numbers from one to infinity being countable infinite and the real numbers between 0 and 1 being uncountable infinite. The trick to the proof comes with being able to count rational numbers from smallest to largest (easy to think about with integers but even with rational numbers it's just integers in the numerator and integers in the denominator so just assign a count to the numerator first and the next count to the denomator and it works). for real numbers if you try to count from one number to the next, there will ALWAYS be an number in between those that you missed and should have counted. blew my brain when the professor showed the proof in class.