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## What is the opposite of zero?

(90 Posts)
CrispyFern Mon 12-May-14 14:43:28

DD asked on the way to school today.
Can anyone help? She's six and a half.

Is it one?

Mon 12-May-14 16:18:02

Wll they dont have one side. They have infinite. But some infinities are bigger than others. Eg all the integers vs all the prime numbers.

insertrandomnamehere Mon 12-May-14 16:18:28

Or one. But if infinite, the same infinity..

Mon 12-May-14 16:20:25

No thats not true. Not all infinities are the same.

Mon 12-May-14 16:25:38

But you are still constantly changing direction, just by varying degrees, wheras you would be constantly changing by the same amount for a circle. So I would say they have the same number of sides, but that ovals have an interesting selection of angles between those sides, where circles have, very boringly, the same angle between all their sides.

Maybe

Mon 12-May-14 16:26:37

I will grant you that the infinite number of integers must indeed be less than the infinite number of numbers, though.

insertrandomnamehere Mon 12-May-14 16:27:05

It depends what you mean by a side, depending on that definition a circle has 0, 1 or infinite sides.

I'd dispute that an oval is 'less' curvy. If the circle and the oval are defined to have infinite sides, then I think that infinity would have the same size, because we're talking about a countable set (ie, natural numbers) Yes infinities have different sizes, but not in this case.

I think. But I suspect this is all meaningless because we'd find it impossible to prove that a circle/oval has infinite sides. I suspect the notion is meaningless because a side is a straight line, circles (strictly speaking) have none.

Mon 12-May-14 16:27:46

Hmm interesting thought
but ifi yiu ars changing angle by fewer degrees wouldnt the arc between any two points have a greater degree of 'straightness'?

Mon 12-May-14 16:29:32

Its the same as the last issue. A circle to my mind is just a erm cant remember the name of the thing which means thing with straight sides...with infinite sides. But strictly speaking the shape approaches a circles as the number of sides approaches infinity.

Mon 12-May-14 16:30:15

What is tye word im looking for? Posh term fir "shape"

Mon 12-May-14 16:31:52

Polygon

insertrandomnamehere Mon 12-May-14 16:32:16

Stealth, yes infinites have different sizes. But in this case we are comparing two discreet sets - ie whole number of sides. These two sets are countably infinite and therefore have the same cardinality (size).

Using your example, the set of primes is the same size as the set of natural numbers. The set of real numbers is larger.

Mon 12-May-14 16:32:16

DONT YOU SWEAR AT ME

Mon 12-May-14 16:32:47

Thats the one, polygon, tha ks

ohmymimi Mon 12-May-14 16:33:33

So glad that's all cleared up then. I'm none the wiser

Mon 12-May-14 16:33:57

Thanks insert. Think I will google countably infinite tonight.
all this stuff is so interesting!

insertrandomnamehere Mon 12-May-14 16:34:30

Actually the infinite set of integers is the same size as the infinite set of all rational numbers, ie including fractions

Mon 12-May-14 16:36:02

So there you go, OP - the answer to your DD's question is "I don't know, DD, ask your teacher - which has more sides, a circle or an oval?"

We delight in sending DS to ask his maths teacher such philosophical questions. She has good discussions with him about them and then swears at me later

insertrandomnamehere Mon 12-May-14 16:36:14

Indeed it is! This was final year stuff by the way so it's by no means basic!

Mon 12-May-14 16:38:07

Erm I did a maths degree too. I just wasnt very good at it! I now work in a job which needs stats, I spent my entire time avoiding stats as it was "dull". I love it now!

insertrandomnamehere Mon 12-May-14 16:39:27

You're right, a polygon with more and more sides will look more and more like a circle, and approaching infinity it will approach a circle. But, like with dividing by zero, it will never quite get there

CommunistLegoBloc Mon 12-May-14 16:41:07

Numbers don't have opposites though, do they? You're only head-scratching because 'zero' has more of a meaning in language than say, 10.

If she'd said 'what's the opposite of 'none'?' you would have said some, or lots.

Mon 12-May-14 16:41:11

Zero.

insertrandomnamehere Mon 12-May-14 16:41:27

I wasn't very good either - thank goodness for being able to take subsidiary modules in lesser subjects to bump up my marks! I now work in a job that has absolutely nothing to do with it!

DeWee Mon 12-May-14 16:42:40

Infinity plus 1 still equals infinity, as does double infinity... as infinity is a concept rather than a number.

I discussed different values of infinity at my Oxford interview. Went via an integration question. Very interesting.

snoggle Mon 12-May-14 16:44:10

I think only descriptive words, ie adjectives and adverbs have opposites don't they? Eg nouns do not. are numbers a sort of noun?

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