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So p > 1.

We can directly get this from (ii) in the problem statement.

How does the conclusion help, though?

*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.

Is that the only possible solution?

Can I have the email to a clam?

What should I be using as k?

Thanks Bob

and a zero sphere is in R.

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:

Thanks, the same trick worked again.

Oh, yes. That works.

Now I need to do the same thing for a 2014-dimensional hypersphere.

**Agnishom**- Replies: 12

Somebody emailed me this problem:

How many such sequences are there such that

(i) a[m*n] = a[m]*a[n] and

(ii) for every m < n, a[m] < B*a[n] for a positive constant B?

The only solution I have so far is the sequence a[n] = n

In the same way, AD should be just sqrt(3). Is it?

bob bundy wrote:

The length CD appears to be √2.r but the true length will be longer in the ratio AD:AB.

I think it should be sqrt(3)*r

Then you can form an equation for r using AD = AB + BC + CD

Bob

How do we get information on CD?

**Agnishom**- Replies: 6

We have a cube of side 2, inside which a sphere or radius 1 is inscribed. What would be the radius of the sphere that would have been inside the cube touching the central sphere and the three walls of the cube?

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

**Agnishom**- Replies: 0

Hi John Green;

I am afraid your conception of 16 year olds is not perfect.

I am 14 and I realise that f(n)=2n does a very good job of bijecting [0,1] to [0,2] which would pretty much imply the same cardinality.

I do not mean to say that there is no truth in your reasoning about kids. You are sort of correct about abstract reasoning but 16 is a little too old. 12 would be okay.

I'd have used the concepts of Aleph-Null and Aleph-One to explain my significant other on different sorts of infinities. Hilbert's hotel is even better.

By the way, do you think that there exists a set whose cadinality is strictly between that of natural numbers and reals.

gourish wrote:

I bet bobbym is a professor isn't he?

The person below will tell.

bobbym wrote:

That is what they say. The last person to say that was?

Zeilberger wrote:

I agree with G.H. Hardy that mathematics is a young man's game (except for the "man" part), but "young" does not mean "under thirty", and not even "under forty". "Young" means, "young at heart", and willing to learn new things and new methodologies and master new technology. If you will follow my advice, I am sure that you would achieve much more than your already very impressive (albeit mostly boring) feats, and your future achievements will not only be technically challending, but also exciting, not just to you and to your thirty cronies, but to all of us common folks.

This note can provide some help finding the book on the web

Hahahha, thanks! Professors are not the only ones having beards, though.

Mathematics is a young man's game.

gourish wrote:

okay... well it says that the book is for B.Sc in math... i am kid in 12th grade... you think it's the right book for me?

Did you know I am in the 11th standard?

Graph theory is a part of combinatorics.

Rewind your life back to Class XI. You would not have believed that solutions to x+y+z=10 is combinatorics. Would you? You'd have thought it is algebra.

In the same way, you probably do not see yet why graph theory is a part of combinatorics, but you'll later.