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#### Alexmahone

##### Active member

- Jan 26, 2012

- 268

I have shown that $f(x)=Cx$ for all rational numbers. How do I use the continuity of $f$ to show it is true for all $x$?

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- Thread starter
- #1

- Jan 26, 2012

- 268

I have shown that $f(x)=Cx$ for all rational numbers. How do I use the continuity of $f$ to show it is true for all $x$?

- Feb 9, 2012

- 118

Having this, remember that rationals are dense in $\mathbb R.$I have shown that $f(x)=Cx$ for all rational numbers.

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- Jan 26, 2012

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Intuitively, I can see that it must be true but I'm having trouble proving it.Having this, remember that rationals are dense in $\mathbb R.$

Every real number is the limit of a sequence of rational numbers.Intuitively, I can see that it must be true but I'm having trouble proving it.

The function is continuous. What continuity and convergent sequences?

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- Jan 26, 2012

- 268

Got it. Thanks!Every real number is the limit of a sequence of rational numbers.

The function is continuous. What continuity and convergent sequences?

- Jan 29, 2012

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