/sci/ - Science & Math

[Anonymous No.3444276]

Hey, /sci/, I need you enlightened and experienced opinion on something! My dad and I were having an argument about the existence of god and somehow, when debating the possibility of "something" coming from "nothing", the number zero was brought up. He did not believe that zero represents "nothing" and then asked me to explain what I thought zero represented. For me, the question took on significance beyond the debate and I kept trying to formulate a precise, generalized definition of the significance of zero in a numeral. Here's what I came up with: "Zero in a numeral shows that no integer less than or equal to the number (represented by the numeral) can not be expressed as a sum of integers multiplied by the base (of that numeral's notation system) raised to the powers corresponding to that zero's place, and all places before it, in a numeral written in positional notation." Was I wrong? How could it have been better? Does that efficiently tell the meaning of zero in a numeral? Was it fatuous? Does the wording earn /sci/'s mathematical rigor seal of approval? It'd be cool if someone knowledgeable about math could tell me. Also, if not that, then let's make this a general math thread.

[Anonymous No.3444292]

That's an overly complicated way to define zero.
There is zero of something, which means there is none of it, which means nothing.
You defined it by how it operates mathematically.
When used in counting, it means nothing.
When used for position, it can mean the origin point. (for example, when you say that someone walked 50 meters, you are saying that, from where they started (0) they walked 50 meters.)

[Anonymous No.3444299]

>>3444276
You're welcome to argue metaphysics and platonic ideals. My answer is "0 is defined as the first Natural Number in the axiomatic framework of ZFC".

[Anonymous No.3444309]

>>3444292
Well, I made sure to restrict my attempt at defining to describing zero's role as a place holder. But... idk.

[Anonymous No.3444322]

>>3444299
See
>>3444309

[Anonymous No.3444369]

Bump, I suppose?
(Capcha somewhat related: theorem (nigger) socilis)

[Anonymous No.3444409]

My answer would be "0 is the symbol for the additive identity of a ring." It is a formalization of the concept of "nothing"

[Anonymous No.3444467]

Zero is one less than one.

[Anonymous No.3444493]

>>3444467

one what?

[Anonymous No.3444499]

>>3444409
Crap, I tried understanding the wiki pages but it was too abstruse. Please excuse my mathematics virginity, but from what I could understand, and from my severely limited perspective, it seems as if "0 is the symbol for the additive identity of a ring." is a tautology? Perhaps I would see it differently if it was described in "layman's" terms. But, regardless, thanks for the help.

[Deist !!fMq8ZXuIWTO No.3444503]

0 is the symbol used to represent the idea of nothing.

You were debating the existence of god and talking about something coming from nothing? I assume you were defending the scientific view and him the religious. Did you ask him where god came from?

wrecked.

[Anonymous No.3444504]

>>3444493
one anything

[Anonymous No.3444519]

zero is in the middle.

[Anonymous No.3444521]

>>3444503
Well, I was making a clumsy analogy to virtual particles and vacuum states to show that something can and does come from nothing. But yes, I did ask him. He could only shrug and repeat the tired old theist's argument about God's "nature".

[Anonymous No.3444527]

>>3444519
Of everything?

[Anonymous No.3444548]

0 can be defined in many different ways depending on the context. but in general i would just say zero is the absence of value.

the history of the number 0 may be interesting to you, op.

http://en.wikipedia.org/wiki/Zero

fun facts: 0 is an even number. 0^0 = 1 (most of the time)

[Anonymous No.3444561]

zero does not represent nothing, that is absolutely wrong. A good definition of zero is complex, but it took humanity a long, long time to figure out the difference between zero and nothing, so don't bring us back in time two thousand years.

[Anonymous No.3444564]

>>3444527
Of whatever you're assigning numbers to (unless you're not using negatives, then zero would be the numerical value of "none").

[Anonymous No.3444584]

>>3444564
-3 is in the middle of -1 and -5.

[Anonymous No.3444588]

>>3444561
So then what is the difference?

[Anonymous No.3444703]

Why can't 0 just be 0? -the absence of a quantity.

[Anonymous No.3444720]

>>3444703
Well it can, but the question was what exactly does zero represent in a positional notation number system.

[Anonymous No.3444723]

wtf the most heated debate ive had with my father was weather to eat mcdonalds or carls jr for lunch

[Anonymous No.3444730]

>>3444723
Your father doesn't love you/ doesn't care about your opinion(thinks you are still a kid)

[Anonymous No.3444752]

>>3444720
The axis between positive and negative infinities.

[Anonymous No.3444767]

>>3444752
"...in a positional notation number system."

[Anonymous No.3444777]

>>3444752
How would that be any different than the axis between "infinities" past 20 and "infinities" before 20 or some other bullshit like that?

[Anonymous No.3444820]

OP's definition isn't that bad for explaining the way 0 works as a place holder. As to what "0" actually means, math doesn't actually I've an answer: in both ZFC and formal number theory in it is the one primitive "undefined" object (in the former it's the empty set, but 0 the natural number 0 is equated with this set). A few basic properties are given by axioms, but since it's an undefined term the natural number 0 we normally think of is just one possible interpretation. The critical property of the empty set is just that there's nothing in it. So you asked this question about the one number- the one object- for which there isn't an answer in the formal framework of set theory. No one's sure what numbers really are outside of set theory, and that's not changing anytime soon since it's a philosophical question.

[Anonymous No.3444828]

Bumping for elucidation.

[Anonymous No.3444833]

>>3444820
Sorry about the typos.

[Anonymous No.3444841]

>>3444820
Just curious; does this post have anything to do with the point that was possibly made here?
>>3444777

[Anonymous No.3444849]

>>3444820
Oh, and thank you.

[Anonymous No.3444979]

>>3444499

This just means that zero has the property that if you add zero to anything in your set you will return that anything

aka x+0=x

We typically think of 0 as being apart of the integers which are a subset of the real numbers but you can have other things which have this property.

Consider a set of two elements E and O such that when you "add" them together this happens

E+E=E, E+O=O+E=O, O+O=E

In this case E takes the property of 0 namely being the additive identity. I believe this satisfies all the group properties as well and you can extend this into a ring with multiplication but w/e.