Philosophy Now Forum

0 is not a number. 0 is just a state of nothing.
Proof: Numbers can have - (negative) signs.
0 cannot be negative or positive.
It follows that 0 is not a number.
Because 0 is not a number, no number can be divided, multiplied subtracted or added with 0.

Zarathustra wrote: ↑Thu Mar 14, 2024 1:26 am 0 is not a number. 0 is just a state of nothing.
Proof: Numbers can have - (negative) signs.
0 cannot be negative or positive.
It follows that 0 is not a number.
Because 0 is not a number, no number can be divided, multiplied subtracted or added with 0.

Wait, you believe numbers exist ?!?

Crazy!

According to the structuralist ontology of mathematics, mathematical objects are exhaustively defined by their place in the structure in which they appear.

Mathematical objects do not possess any intrinsic properties but are defined by their external relations in the structure.

In abstract algebra, 0 is typically used to denote the identity element for addition and the absorbing element for multiplication.

Zero is therefore, merely a template placeholder in the algebraic structure at hand, outside of which it has absolutely no meaning.

But then again, according to the formalist ontology, a complete algebraic structure has no meaning either. Statements of mathematics can be considered to be statements about the consequences of the manipulation of strings.

They are not a body of propositions representing an abstract sector of reality, are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all.

Hence, the question if zero is a number, is irrelevant, because "being a number" is not an intrinsic property of any particular symbol but a property attached to a template placeholder in an otherwise equally meaningless algebraic structure.

godelian wrote: ↑Thu Mar 14, 2024 6:56 am In abstract algebra, 0 is typically used to denote the identity element for addition and the absorbing element for multiplication.

So 0 is like a roll of paper towels?

Zarathustra wrote: ↑Thu Mar 14, 2024 1:26 am 0 is not a number. 0 is just a state of nothing.
Proof: Numbers can have - (negative) signs.

a = -0

5 + a = 5-0 = 5

Oh look it still works!

wtf wrote: ↑Thu Mar 14, 2024 8:18 pm

godelian wrote: ↑Thu Mar 14, 2024 6:56 am In abstract algebra, 0 is typically used to denote the identity element for addition and the absorbing element for multiplication.

So 0 is like a roll of paper towels?

Take for example the natural numbers and its canonical axiomatization:

https://en.m.wikipedia.org/wiki/Peano_axioms

In mathematical logic, the Peano axioms (/piˈɑːnoʊ/,[1] [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano.
...
The first axiom states that the constant 0 is a natural number:

0 is a natural number.
...
The structure (N, +) is a commutative monoid with identity element 0.
...
A model of the Peano axioms is a triple (N, 0, S), where N is a (necessarily infinite) set, 0 ∈ N and S: N → N satisfies the axioms above.

The symbol "0" is one of the non-logical symbols in the canonical theory of the natural numbers (PA). In this algebraic structure, it is axiomatized to be itself a natural number.

The symbol "0" is a template placeholder in a particular structure and its properties are exclusively derived from its place in it. It is meaningless to discuss this symbol in absence of any structure.

Atla wrote: ↑Thu Mar 14, 2024 8:34 pm

Zarathustra wrote: ↑Thu Mar 14, 2024 1:26 am 0 is not a number. 0 is just a state of nothing.
Proof: Numbers can have - (negative) signs.

a = -0

5 + a = 5-0 = 5

Oh look it still works!

Depending on the parser at hand, the token stream "5+-0" will generate a syntax error. But then again, many won't. It depends on the regular expression matching negative numbers. It is usually surprisingly liberal.

godelian wrote: ↑Fri Mar 15, 2024 1:53 am Take for example the natural numbers and its canonical axiomatization:

So you refuse to engage with what I said? You said 0 is the absorbing element. I asked you if that means 0 is like a roll of paper towels. And you refuse to engage. Do paper towels absorb or not? And if they do, how do they differ from 0?

Don't shoot, I'm only the Peano player.

if 0 isn't a number, what's the difference between 1 and 10 and 100?

-Imp

wtf wrote: ↑Thu Mar 14, 2024 8:18 pm

godelian wrote: ↑Thu Mar 14, 2024 6:56 am In abstract algebra, 0 is typically used to denote the identity element for addition and the absorbing element for multiplication.

So 0 is like a roll of paper towels?

Dunkin doughnuts

Atla wrote: ↑Thu Mar 14, 2024 8:34 pm

Zarathustra wrote: ↑Thu Mar 14, 2024 1:26 am 0 is not a number. 0 is just a state of nothing.
Proof: Numbers can have - (negative) signs.

a = -0

5 + a = 5-0 = 5

Oh look it still works!

a= -0
It just proves that 5 + a = 5 - 0 = 5 was a waste of time.

godelian wrote: ↑Fri Mar 15, 2024 2:00 am

Atla wrote: ↑Thu Mar 14, 2024 8:34 pm

Zarathustra wrote: ↑Thu Mar 14, 2024 1:26 am 0 is not a number. 0 is just a state of nothing.
Proof: Numbers can have - (negative) signs.

a = -0

5 + a = 5-0 = 5

Oh look it still works!

Depending on the parser at hand, the token stream "5+-0" will generate a syntax error. But then again, many won't. It depends on the regular expression matching negative numbers. It is usually surprisingly liberal.

Most computer programs would have generated syntax error when seeing "-0".

Impenitent wrote: ↑Sat Mar 16, 2024 12:33 am if 0 isn't a number, what's the difference between 1 and 10 and 100?

-Imp

The 0s in 10 and 100 are not standalone 0s, but parts of the number 10 and 100.

Exactly. It's just a place holder so u can continue adding past nine without repeating a previous figure. It would be impossible to create a unique figure for all the numbers after nine, so we repeat the same sequence but add a place so we can double up the numbers to create bigger numbers. Each time we run through a single or double set of 1 -9s, we add another place and make a triple set of 1-9s. It's all so tediously boring and mathematic, math is.

wtf wrote: ↑Fri Mar 15, 2024 10:50 pm

godelian wrote: ↑Fri Mar 15, 2024 1:53 am Take for example the natural numbers and its canonical axiomatization:

So you refuse to engage with what I said? You said 0 is the absorbing element. I asked you if that means 0 is like a roll of paper towels. And you refuse to engage. Do paper towels absorb or not? And if they do, how do they differ from 0?

Don't shoot, I'm only the Peano player.

5 * 0 = 0. Multiplying any number by zero results in zero. So, zero is said to "absorb" the multiplication. This is a characteristic of the neutral element for the addition.

If there exists an element x as such that for every element a of the domain, a + x = a, then multiplying by this neutral element x will be absorbed into x, i.e. a * x = x.

It works not just with numbers. It will for example also work in a ring of elliptic-curve points. In fact, it will work in a ring or a field of any type of objects.