Are You Talking About Ordinal Numbers?

Calculus Level 2

Take a certain positive number and square it to get a distinct number, then square it again to get yet another distinct number, and then again, and so on indefinitely.

If the limiting value converges to a finite number x , x, what is x ? x?

0 1 2 This is an impossible scenario

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1 solution

Alex Li
Apr 21, 2016

Relevant wiki: Nested Functions

Pick a positive number.

If the number you pick is greater than 1, than it will become bigger at an increasing rate.

If the number you pick is equal to 1, it will stay at 1, not giving distinct numbers.

If the number you pick is less than 1, it will continually get smaller, but by a smaller amount. For example, if you pick 1/2:

1/2 -> 1/4 -> 1/16 -> 1/256...

It is easy to see that it converges at 0.

Since zero is neither a positive number nor a negative one, the correct answer should be: "This is an impossible scenario".

Reemon Spector - 5 years, 1 month ago

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The question states that "If the limiting value converges to a finite number .... ", so 0 is just an infimum .

Pi Han Goh - 5 years, 1 month ago

It doesn't exactly become 0. It just comes closer and closer to 0 but never becomes 0. It will become 0 after infinite terms which is no value, if you say numbers beyond 1 and a 1000 zeroes is infinity, I can always find a number greater than that by adding maybe 1. Infinity is what no can ever reach, it's beyond which we can count.

Kushagra Sahni - 5 years, 1 month ago

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