People don't understand what a manifold is or what it means to be homeomorphic.

Careful here! {ben} is a singleton in the powerset {P(people)}

Don't be silly, ben's not people! ben just thinks he's people. Ben's really a figment of my imagination. Sorry ben, I was going to tell you earlier but I just didn't have the heart to break it to you before now. ;-)

]]>I Fully Understand the Problem!

I strongly doubt that.

I don't "strongly doubt it", I *know* it

People don't understand what a manifold is or what it means to be homeomorphic.

Careful here! {ben} is a singleton in the powerset {P(people)}

]]>if you take timbits (doughnut holes, or whatever else you call them)

Munchkins.

I Fully Understand the Problem!

I strongly doubt that.

Far Better from the Start to Give actual Examples! and Simplified Math to explain the Problem!

People can't understand the actual examples. People don't understand what a manifold is or what it means to be homeomorphic.

]]>At Last we Agree on Something!...........................................................................................

]]>Some Doughnuts can be the Same Round Shape as an Apple!!

Yes, the entire "proof" clearly falls apart if you take timbits (doughnut holes, or whatever else you call them) into account. Even jelly-filled doughnuts would disrupt this proof! Clearly PoincarĂ© wasn't thinking clearly and his entire work should be thrown out the window for these heinous oversights. ;-)

]]>Quote:" But you seem not to understand that what you you call "apples" (2-sphere) and "doughnuts" (2-torus) are classic examples of 2-manifolds.

A.R.B

Some Doughnuts can be the Same Round Shape as an Apple!!

]]>But in a Sarcastic way I'm showing How Math Simplified Examples! can make the Situation Worse! by Giving Examples Using Items like Rubber Bands! Apples! Doughnuts!

Far Better from the Start to Give actual Examples! and Simplified Math to explain the Problem!

A.R.B

]]>The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )

But you seem not to understand that what you you call "apples" (2-sphere) and "doughnuts" (2-torus) are classic examples of 2-manifolds. The P. conjecture is relatively easy to prove in the 2-dimensional case, exceptionally difficult for the 3-manifold case. Hence the prize. Ricky has it right; this is the PoincarĂ© conjecture:

Ricky wrote:

Every simply connected closed three-manifold is homeomorphic to the three-sphere.

So, before you start spouting off your nonsense, make sure that (at the very least) you understand what a manifold is, what it means for it to be connected and what the word homeomorphic means. Until you have that under your belt, you are not qualified to comment.

]]>The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )

Again Anthony, that's not the original problem. That is a description of the problem given to people who are not literate in topology. This is the Poincare conjecture:

Every simply connected closed three-manifold is homeomorphic to the three-sphere.

Do you now see why we don't tell people the actual mathematical problem? Almost no one would understand it!

]]>Have and Gave is the Start of the Problem ( 2 + 2 = 4 )

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