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Crazy boy [7]
3 years ago
7

For each $n \in \mathbb{N}$, let $A_n = [n] \times [n]$. Define $B = \bigcup_{n \in \mathbb{N}} A_n$. Does $B = \mathbb{N} \time

s \mathbb{N}$? Either prove that it does, or show why it does not.
Mathematics
1 answer:
andre [41]3 years ago
4 0

Answer:

No, it is not.

Step-by-step explanation:

The set C = \mathbb{N} \times \mathbb{N} contains every ordered pair of Natural numbers, while B only contains those pairs in which both values in each entry are the same. Therefore, C is a bigger set than B, but B is not equal to C because for example C contains [1] \times [2] and B doesnt because 1 is not equal to 2.

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