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Tagged with natural-numbers soft-question
11
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207
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Do we have complete understanding of $\mathbb N$?
We have some understanding of natural numbers. We have PA theory and we believe that $\mathbb N$ is one of the PA models. But PA can't prove some statements about $\mathbb N$ even though they are true ...
- 157
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How are numbers assigned to a group of real life objects?
I hope I don't come off as dense but suppose I constructed (informally) the decimal number system assuming the existence of symbols, 1-9 and defining the operation of addition on it with usual ...
- 43
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How do mathematicians know if they are extending the theory of natural numbers in the right direction?
According to Godel's incompleteness theorem, any formal system can never deduce all the truths about the set of natural numbers. Hence, to deduce more truths than we were able to before, we extend our ...
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13
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Examples of polynomial injections $f:\mathbb{N}\times \mathbb{N}\to \mathbb{N}$
I've seen that there are polynomial bijections $f:\mathbb{N}\times \mathbb{N}\to \mathbb{N},$ for example $f(m,n)=\frac{1}{2}(n+m)(n+m-1)+m.$ I'm looking for more examples of injective polynomials ...
- 4,794
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Define a geometry based on a pseudometric in which the distance between distinct primes is zero?
Consider a pseudometric on $\Bbb N$ by $d(p_k,p_n)=0;$ else $d(x,y)=|x-y|.$ Here $p_k,p_n$ are distinct primes.
Edit 5/14/2020: From the comment below the definition I gave does not satisfy the ...
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Hierarchy of subsets of $\mathbb{N}$
I was wondering if there is an interesting way to build an "hierarchy" of natural numbers subsets in a transfinite sequence: $$(U_\alpha)_{\alpha < \lambda} \quad \text{with } U_\alpha \subset\...
- 2,611
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Is there a general mathematical method that determines whether any sequence of natural numbers is generated by a particular mathematical law?
My question is:
In mathematics is there a general method that determines whether any sequence of natural numbers is generated by a particular mathematical law/function/closed-form expression/...
- 477
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6
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What is a number in math? [closed]
Before I begin, let me give you so background. I previously asked a question on "How to prove that −x is not equal to x just because they yield the same result when in $x^2$". This got me thinking. ...
- 2,292
6
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4
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Counting numbers vs Natural numbers; Peano Axioms
I can feel that my question is going to be a somewhat lengthy one, but I will try my best to deliver it in as short a form as I can manage.
So to begin, I've always thought that the numbers such as 1,...
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10
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4
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Should $\mathbb{N}$ contain $0$? [closed]
This is a classical question, that has led to many a heated argument:
Should the symbol $\mathbb{N}$ stand for $0,1,2,3,\dots$ or $1,2,3,\dots$?
It is immediately obvious that the question is not ...
- 12.7k
4
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Interesting or non-obvious finite subsets of the natural numbers
I was recently explaining to someone how to prove that there are infinitely many prime numbers, and I mentioned to them that it's not immediately obvious, upon first encountering the natural numbers, ...
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