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Originally Posted by Rndm_Perfection
To further explain...
9 x .9 is exactly .9 less than 9... which is 8.1
9 x 9.99 is exactly .09 less than 9... which is 8.81
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can you phrase this differently for the sake of clarity. 9 x 9.99 is 89.91, which is exactly .09 less than 90. Maybe you meant to say 9 x .999 is 8.991 which is exactly less than 9?
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If this continued "infinitely", then .999 repeating multiplied by 9 would have to be exactly .0(repeating) less than 9. And I assume you know .0(repeating) equals zero, and that you cannot tack a number (such as 9, in this instance) to the end of an infinite.
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The distinction of infinity is the difference. Your argument that there is no conceivable number between .999~ repeating and 1 is the clincher since a number cannot be tacked at the end of an infinite. Could there be a number to meet the infinitesimally receding value of the difference between .999~ and 1. Apparently not in a mathematical expression. So I'll admit I was wrong in an arithmetic sense. It's just a matter of grasping the concept of infinity (which I freely admit that I don't). But I keep thinking of a graph that infinitely approaches 1 as its limit.