which of the following statement is True ?
1. There exist a bijective function from R−Q to R
2 There exist a bijective function from Q to Z×N
3 There does exists strictly increasing function from Z to N
4.There does exists strictly increasing onto function from Z to N
I thinks only option 2 is true because countable map to countable
Answer
1) is true since R∖Q has same cardinality as R
2) is true.
3) and 4) are false. Suppose there is a strictly incerasing function f:Z→N. Let f(0)=n. Then f(−1),f(−2),.... satisfy the inequalities $... f(-n)
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