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You're welcome.

bob bundy wrote:

Stefy wrote:Can you prove that statement?

You just extrapolated. It doesn't prove that it must be that formula.

EDIT: Found this:http://www.jstor.org/stable/2322314?seq … b_contents

Agnishom wrote:

According to your definition, the zero sphere is in R.I'd rather have the zero sphere to be the trivial sphere {0} in {0} and 1-sphere in R.

Well, I guess you'll have to readjust to this definition. It makes more sense when you look at it this way: The 1-sphere is a curved line with only 1 "dimension". The 2-sphere is a surface with 2 "dimensions".

bob bundy wrote:

Let

All sequences must have this form.

Can you prove that statement?

Well, I think so. I think there are more, but these are all just for B=1.

Any positive real number will do.

bob bundy wrote:

That's a mighty fine geogebra demonstration Agnishom. I am well impressed!

Stefy wrote:An n-sphere is the set of all points in n+1 dimensional space

So a 1-sphere is in 2-D space.

Bob

Yes.

Because there are no non-trivial circles in the trivial space {0}.

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.

1-sphere, sorry.

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 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

DeanPemberton wrote:

Math is a subject that is totally based on formulas there are thousands of formulas used in maths, it is not possible to remember all of those formulas you can take help from some apps like Math formulas and Physics formulas.

I don't exactly agree with that. I think it's more about ideas than exact formulas.

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.

Well, this guys name is August.

I think it needs to satisfy both.

Agnishom wrote:

anonimnystefy wrote:It's a circle, but the inside is not fully collored.

What is the point?

point

n.

1. A sharp or tapered end: the point of a knife; the point of the antenna; EDIT: the point of the head.

Is this what you mean?

bobbym wrote:

One by one? So that is where I have been going wrong.

Not literally. Maybe a phrase would be inside out.

It's a circle, but the inside is not fully collored.

Have you tried using the rules of differentiation?

I've learned that there is a very interesting and somewhat natural measure of graph connectedness which also has some nice algebraic properties.

Also, I'm looking to better myself in the study of non-standard analysis, so I've been learning about that a bit too.

No problemo. Did you do the other one?