The recursive function for a sequence is given below.
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That easiliy false. You can prove this by observing that all integers are, in particular, rational numbers. So, for instance, you can think of 4 as , so
And obviously, you have
It is true that the square of every rational number between 0 and 1 is smaller than the number itself.
But since not all rational numbers are between 0 and 1, the general claim is false.