Definition:Integral Multiple/Real Numbers
< Definition:Integral Multiple(Redirected from Definition:Integer Multiple)
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Definition
Let $x, y \in \R$ be real numbers.
Then $x$ is an integral multiple of $y$ if and only if $x$ is congruent to $0$ modulo $y$:
- $x \equiv 0 \pmod y$
That is:
- $\exists k \in \Z: x = 0 + k y$
Also known as
An integral multiple is usually known, in this context, as an integer multiple.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.5$. Congruence of integers: Example $38$