History of notation of sets: Why $\mathbb{Z}$ and $\mathbb{Q}$ for integers and rationals, but $\mathbb{R}$ and $\mathbb{N}$ for reals and naturals?

Question

Why do we denote set of integers as $\mathbb Z$ and set of rationals as $\mathbb Q$, although we use $\mathbb R$ for real, $\mathbb N$ for natural numbers, etc. What's the reason or history behind it?

Answer 1

From the comments above.

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The notation $\mathbb{Z}$ for the set of integers comes from the German word Zahlen for numbers.

The notation $\mathbb{Q}$ for the set of rational numbers was chosen to indicate that $\mathbb{Q}$ is the set of quotients of integers.

You might find this site informative on the history of these notations.