How about ANY FINITE SEQUENCE AT ALL?

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8 points

Exceptions are infinite. Is that rare?

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1 point

Yes. The exceptions are a smaller cardinality of infinity than the set of all real numbers.

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1 point

Yes, compared to the infinitely more non exceptions. For each infinite number that doesn’t contain the digit 9 you have an infinite amount of numbers that can be mapped to that by removing all the 9s. For example 3.99345 and 3.34999995 both map to 3.345. In the other direction it doesn’t work that way.

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13 points

Rare in this context is a question of density. There are infinitely many integers within the real numbers, for example, but there are far more non-integers than integers. So integers are more rare within the real.

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-8 points

There is not density in infinity

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10 points

I think you mean “I don’t understand density in infinity”.

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