Decimal Expansion Homework: Terminating & Non-Terminating 9's

cragar
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Homework Statement


How many decimal expansions terminate in an infinite string of 9's?
How many dont?

The Attempt at a Solution


If we have a number terminate with an infinite amount of 9's then it will be a rational number.
So there would be countably many of these.

And since irrational numbers do not end with all 9's then their would be
uncountably many of them that do not.
 
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cragar said:

Homework Statement


How many decimal expansions terminate in an infinite string of 9's?
How many dont?

The Attempt at a Solution


If we have a number terminate with an infinite amount of 9's then it will be a rational number.
So there would be countably many of these.

And since irrational numbers do not end with all 9's then their would be
uncountably many of them that do not.

That's the right idea.
 

Thread 'Finding the nth roots of a complex number'

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