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2
questions
2
votes
3
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How to show that this set is finite?
Let $m \in \mathbb{N}$
For $\alpha = (\alpha_{1},...,\alpha_{m}) \in \mathbb{N}_{0}^{m}$, let $|\alpha|:= \alpha_{1}+...+\alpha_{m}$
Is the set $\{\alpha \in \mathbb{N}_{0}^{m}: |\alpha|\leq k\}$ ...
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7
votes
1
answer
2k
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Can the natural numbers be uncountable?
Definition of a countable set, from Stanford, as I didn't want to quote Wikipedia:
Definition. A set S is countable if |S| = |N|.
Thus a set S is countable if there is a one-to-one mapping of Num ...
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