Discussion Overview
The discussion revolves around the international notations for various sets of numbers, including integers, even numbers, odd numbers, prime numbers, composite numbers, and cube numbers. Participants explore the existing notations and inquire about single-letter representations.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants state that the international notations for natural numbers, whole numbers, rational numbers, real numbers, and complex numbers are represented as N, Z, Q, R, and C, respectively.
- One participant proposes that the notation for natural numbers and zero can be represented as $\mathbb Z_{\ge 0}$, $\mathbb Z \setminus \mathbb Z^-$, or $\mathbb N \cup \{0\}$, noting the ambiguity of $\mathbb N$ regarding the inclusion of zero.
- Even numbers are suggested to be represented as $2\mathbb Z$ or $\{2k : k\in\mathbb Z\}$, while odd numbers can be denoted as $\{2k+1 : k\in\mathbb Z\}$ or $\mathbb Z \setminus 2\mathbb Z$.
- Prime numbers are described as $\{k : k\text{ is prime}\}$ or simply 'the set of primes', with some texts potentially using $\mathbb P$ or $P$ for primes, though this is not an international convention.
- Composite numbers are similarly represented as $\{k : k\text{ is composite}\}$ or 'the set of composite numbers'.
- Cube numbers are proposed to be represented as $\{k^3 : k\in \mathbb Z\}$ or $\{k^3\}$ in contexts specifically about integers.
- One participant inquires about the existence of single-letter notations for these sets, to which another participant responds that there are only a few single-letter sets, such as $\mathbb H$ for quaternions and $I$ for the unit interval [0,1].
Areas of Agreement / Disagreement
Participants generally agree on the notations for the various sets discussed, but there is no consensus on the existence of single-letter representations for all sets, as the responses indicate limited examples.
Contextual Notes
The discussion highlights the ambiguity in the notation for natural numbers regarding the inclusion of zero and the lack of widely accepted single-letter notations for many of the specified sets.