Questions tagged [natural-numbers]
For question about natural numbers $\Bbb N$, their properties and applications
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What is an example of a bijective function f: Z to N that isn't piecewise?
Like without using if even or odd. Like how you can define a bijection $f\colon\mathbb{N}\to\mathbb{Z}$ by is $f(n)=\lfloor n/2\rfloor\cdot(-1)^n$.
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Defining $A \in \mathcal{P}(\Bbb N \times\Bbb N)$ such that it is not any member of a countable subset $M \subseteq \mathcal{P}(\Bbb N \times \Bbb N)$
$
\newcommand{\N}{\mathbb{N}}
\newcommand{\P}{\mathcal{P}(\N \times \N)}
\newcommand{\set}[1]{\left\{ #1 \right\}}
\newcommand{\i}{^{(i)}}
\newcommand{\x}{^{[x]}}
\newcommand{\y}{^{[y]}}
\newcommand{\...
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How to find the smallest $a,b ∈ N$ that solve a single equation
Im trying to find a method that solves the equality of two quadratic equations with the constraint of $a$ and $b$ being natural numbers, the only way I know is trying value per value, but I was ...
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If $a|N$ and $b|N$ where $a,b$ are coprime , is it necessary that $(a \times b) |N$? [duplicate]
In the above statement N , a , b are natural numbers . I was wondering whether the above statement is always true . If it is always true will anyone give me a simple reason or proof for it ? Please ...
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Proving commutativity of multiplication
I am trying to prove Lemma 2.3.2 in Tao's analysis text: that for any two natural number, $n$ and $m$, we have $n \times m = m \times n$. I only have the properties of the natural numbers and addition ...
user465188
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What is the intuitive meaning of natural numbers as constructed in ZF set theory?
My understanding is that in elementary set theory, the natural numbers are defined so that $0 = \emptyset$ and $n+1 = n \cup \{ n \}$. I understand that this gives us some very pleasant properties ...
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Find the smallest natural number that satisfy $13^N = 1 \pmod {2013}$
Moderator Note: This is a current contest question on Brilliant.org.
Find the smallest natural number that satisfy:
$$13^N = 1 \pmod {2013}$$
My idea is to use the Fermat's little theorem for ...
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$\omega^\omega$ correspondence with $\mathbb R$-irrationality
Here in the second comment I do not understand why $\omega^\omega$ corresponds to irrational numbers? :
In my experience one typically identifies $ω^ω$ with the irrational elements of R; and then we ...
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Can we modify the Peano axioms like this? [closed]
I am wondering if the following modifications of the Peano axioms result in a set of axioms equivalent to the Peano axioms, in the sense that any set of numbers satisfies these modified axioms if and ...
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