difference of zero, circle and alphabet O

pari_alf · 2014-12-05 20:10:10

What is the difference of circle, zero and alphabet O?

Agnishom · 2014-12-05 20:23:22

A circle is the set of all points on a plane which are equidistant from a given point.

Zero is {}.

O is a letter.

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Well, we use a circle to represent the two later things but it is just a notation.

pari_alf · 2014-12-10 13:33:34

But i think in shape wise,.. both are same. .

Agnishom wrote:

A circle is the set of all points on a plane which are equidistant from a given point.
Zero is {}.
O is a letter.
---
Well, we use a circle to represent the two later things but it is just a notation.

pari_alf · 2014-12-10 13:34:46

similarly, shape wise.. there is not a difference between 7 and > sign. both look similar in shape wise.

What you guys give opinion on it.

thanks

David · 2014-12-10 15:28:42

First of all, shape wise, they somewhat look the same but they are NOT. They also represents different things and they also have different roles.
0 is a number that is neither positive nor negative.
o is a letter used in languages like English, French or any language with Latin origin.
The circle however, is a shape. It's a geometrical shape.

For the 7 and the greater than sign, they don't look the same. They have different roles and uses too.
7 is a number {7}
> this is a sign used to represent "being greater than" as in a > b (a is greater than b).

Agnishom · 2014-12-10 18:15:23

How does the shape matter?

It is just an way to represent a concept

Bob · 2014-12-10 21:19:29

If the shapes are the same, you might get confused about which was meant. On my laptop a zero looks like this 0 and a letter 'oh' looks like this O.

For me there is a difference, but, as it will depend on how your computer renders them, you may be looking at the same thing. You can distinguish them by checking out the ASCII values. The number zero is ASCII 48. The letter 'oh' is 79 when in capital and 111 in small. [note: 79 + 32 = 111. This is not a coincidence. All smalls are capital + 32]

A circle will not be an oval shape, so for me, the letter looks like a circle.

In number theory, zero is defined as the additive identity, ie. it has the property a + 0 = a for all a.

There is also something called 'big O' notation: http://en.wikipedia.org/wiki/Big_O_notation

Bob

Agnishom · 2014-12-10 21:40:11

Alternatively we can define 0 to be the cardinality of the null set.

Some people define it as the null set itself.

Bob · 2014-12-10 21:48:06

'cardinality' is fine, but I think it limits you to {counting numbers}. Number theory is for {reals}

But either definition is good. Can you prove that each implies the other ?

Bob

Agnishom · 2014-12-10 23:46:21

I and stefy had a conversation about it. I guess we start by constructing a successor function and then defining addition.

pari_alf · 2014-12-14 19:56:32

Well, i was just considering only in context of shape.
Shape wise they might look similar.
anyway.. thanks guys for having a very nice discussuion

zetafunc · 2014-12-14 22:35:26

pari_alf wrote:

Well, i was just considering only in context of shape.
Shape wise they might look similar.
anyway.. thanks guys for having a very nice discussuion

Well, as shapes, they are homeomorphic. We define a homeomorphism as follows.

If f satisfies these conditions, then we say that A and B are homeomorphic.

Intuitively, think about being able to 'continuously deform' one shape into the other.

Last edited by zetafunc (2014-12-14 22:37:58)

Bob · 2014-12-15 00:41:21

hi zetafunc.

Excellent! All we need now is for bobbym to provide a deforming procedure in geogebra.

Bob

anonimnystefy · 2014-12-15 01:40:47

bob bundy wrote:

'cardinality' is fine, but I think it limits you to {counting numbers}. Number theory is for {reals}
But either definition is good. Can you prove that each implies the other ?
Bob

You can construct it both ways and it would be the same (up to an isomorphism ).

Also, zero isn't defined as the cardinality of {}. It's defined as the empty set itself.

Last edited by anonimnystefy (2014-12-15 01:43:01)

Agnishom · 2014-12-15 03:01:23

bob bundy wrote:

hi zetafunc.
Excellent! All we need now is for bobbym to provide a deforming procedure in geogebra.
Bob

That is hardly nexessary.

We can truly experimentally prove the existence of the homeomorphism with a soft rubber ball

Bob · 2014-12-15 06:50:04

Sorry to be picky, but a soft rubber ball is 3 dimensional and his shapes are 2-D. Have you got a 2-D soft rubber ball by any chance ?

Bob

anonimnystefy · 2014-12-15 10:43:39

bob bundy wrote:

Sorry to be picky, but a soft rubber ball is 3 dimensional and his shapes are 2-D. Have you got a 2-D soft rubber ball by any chance ?
Bob

Sorry to be picky, but his shapes are 1-D

Bob · 2014-12-15 10:54:04

Oh ha!

Since when has a circle been 1-D ? Try drawing one on a line.

Bob

anonimnystefy · 2014-12-15 11:59:38

Sorry, confused it with the nomenclature 1-circle.

Also, if looked at as a vector space with the operation being multiplication, it really is a 1-dimensional space.

Bob · 2014-12-15 21:03:18

1-circle

What is this, please ? I googled it and got, as the first hit, a chance to buy one!

Bob

anonimnystefy · 2014-12-15 23:32:06

1-sphere, sorry.

Bob · 2014-12-16 00:45:48

Substitute 1-sphere in my question about 1-circle.

Bob

Agnishom · 2014-12-16 04:23:40

I think an n-sphere is defined to be the set of all n-points in n-space that is equidistant from a fixed point.

anonimnystefy · 2014-12-16 04:50:16

I don't think there exists a notion of an n-point.

An n-sphere is the set of all points in n+1 dimensional space with a defined measure for which the distance from 0 is equal.

Agnishom · 2014-12-16 05:04:15

Why'd you want to define it as the points in n+1 space instead of n-space?

All we need now is for bobbym to provide a deforming procedure in geogebra.

I created a deformation in geogebra:

Last edited by Agnishom (2014-12-16 05:05:47)

Math Is Fun Forum

#1 2014-12-05 20:10:10

difference of zero, circle and alphabet O

#2 2014-12-05 20:23:22

Re: difference of zero, circle and alphabet O

#3 2014-12-10 13:33:34

Re: difference of zero, circle and alphabet O

#4 2014-12-10 13:34:46

Re: difference of zero, circle and alphabet O

#5 2014-12-10 15:28:42

Re: difference of zero, circle and alphabet O

#6 2014-12-10 18:15:23

Re: difference of zero, circle and alphabet O

#7 2014-12-10 21:19:29

Re: difference of zero, circle and alphabet O

#8 2014-12-10 21:40:11

Re: difference of zero, circle and alphabet O

#9 2014-12-10 21:48:06

Re: difference of zero, circle and alphabet O

#10 2014-12-10 23:46:21

Re: difference of zero, circle and alphabet O

#11 2014-12-14 19:56:32

Re: difference of zero, circle and alphabet O

#12 2014-12-14 22:35:26

Re: difference of zero, circle and alphabet O

#13 2014-12-15 00:41:21

Re: difference of zero, circle and alphabet O

#14 2014-12-15 01:40:47

Re: difference of zero, circle and alphabet O

#15 2014-12-15 03:01:23

Re: difference of zero, circle and alphabet O

#16 2014-12-15 06:50:04

Re: difference of zero, circle and alphabet O

#17 2014-12-15 10:43:39

Re: difference of zero, circle and alphabet O

#18 2014-12-15 10:54:04

Re: difference of zero, circle and alphabet O

#19 2014-12-15 11:59:38

Re: difference of zero, circle and alphabet O

#20 2014-12-15 21:03:18

Re: difference of zero, circle and alphabet O

#21 2014-12-15 23:32:06

Re: difference of zero, circle and alphabet O

#22 2014-12-16 00:45:48

Re: difference of zero, circle and alphabet O

#23 2014-12-16 04:23:40

Re: difference of zero, circle and alphabet O

#24 2014-12-16 04:50:16

Re: difference of zero, circle and alphabet O

#25 2014-12-16 05:04:15

Re: difference of zero, circle and alphabet O

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