Question 1. [ 25 Marks] 1.1. Find a bijective function to show that the following intervals of real numbers have the same cardinality.
[0,\infty ),(-\infty ,0)
. 1.2. Prove that
N^(k)=N\times N\times cdots\times N
(
k
factors) is countably infinite. 1.3. Find a tan function to illustrate that:
|(0,1)|=|R|.

Question

Question 1. [ 25 Marks] 1.1. Find a bijective function to show that the following intervals of real numbers have the same cardinality.

[0,\infty ),(-\infty ,0)

. 1.2. Prove that

N^(k)=N\times N\times cdots\times N

(

k

factors) is countably infinite. 1.3. Find a tan function to illustrate that:

|(0,1)|=|R|.

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Expert Answer to - Question 1. [ 25 Marks] 1.1. Find a bijective function to show that the following intervals of real

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Solution for - Question 1. [ 25 Marks] 1.1. Find a bijective function to show that the following intervals of real

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