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**Let f:**

**R**[tex]\rightarrow[/tex]**R**be a non-decreasing function. Suppose that f maps**Q**to**Q**and f:**Q**[tex]\rightarrow[/tex]**Q**bijection. Prove that f:**R**[tex]\rightarrow[/tex]**R**is continuous, one to one and onto.Hello everyone, I have been staring at this statement for a while now and I just don't understand it, hence I can't even begin to prove it. Can someone explain to me in different words what am I being asked to do. Is f the same same function and

**Q**[tex]\rightarrow[/tex]

**Q**is somehow "inside"

**R**[tex]\rightarrow[/tex]

**R**. I don't understand how f could be the same if

**R**and

**Q**don't have the same cardinality, or in other words-I am lost. Any type of help is greatly appreciated.

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