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Shahrooz
Shahrooz
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One of the strange proofs (among the other beautiful proof) in the book "Proofs from the book" is the fifth one, which uses a special topology on the set of integer numbers, to prove there are infinite prime numbers.

My question is:

Is this method special just for this case, or is there anything deeper and this technique (or its generalization) can be used for some other kinds of problems?

A related question (by @ToddTrimble comment):

https://mathoverflow.net/questions/42589/is-fürstenbergs-topology-useful

One of the strange proofs (among the other beautiful proof) in the book "Proofs from the book" is the fifth one, which uses a special topology on the set of integer numbers, to prove there are infinite prime numbers.

My question is:

Is this method special just for this case, or is there anything deeper and this technique (or its generalization) can be used for some other kinds of problems?

One of the strange proofs (among the other beautiful proof) in the book "Proofs from the book" is the fifth one, which uses a special topology on the set of integer numbers, to prove there are infinite prime numbers.

My question is:

Is this method special just for this case, or is there anything deeper and this technique (or its generalization) can be used for some other kinds of problems?

A related question (by @ToddTrimble comment):

https://mathoverflow.net/questions/42589/is-fürstenbergs-topology-useful

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YCor
YCor
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One of the strange proofproofs (among the other beautiful proof) in the book "Proofs from the book""Proofs from the book" is the fifth one, which useuses a special topology on the set of integer numbernumbers, to prove there are infinite prime numbers.

My question is:

Is this method special just for this case, or is there are somethinganything deeper and this technique (or its generalization) can be used for some other kinds of problems?

One of the strange proof (among the other beautiful proof) in the book "Proofs from the book" is the fifth one which use special topology on integer number to prove there are infinite prime numbers.

My question is:

Is this method special just for this case or there are something deeper and this technique (or its generalization) can be used for some other kinds of problems?

One of the strange proofs (among the other beautiful proof) in the book "Proofs from the book" is the fifth one, which uses a special topology on the set of integer numbers, to prove there are infinite prime numbers.

My question is:

Is this method special just for this case, or is there anything deeper and this technique (or its generalization) can be used for some other kinds of problems?

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Shahrooz
Shahrooz
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Topology and infinite number of primes

One of the strange proof (among the other beautiful proof) in the book "Proofs from the book" is the fifth one which use special topology on integer number to prove there are infinite prime numbers.

My question is:

Is this method special just for this case or there are something deeper and this technique (or its generalization) can be used for some other kinds of problems?