3 ms·
There is such a thing as 0.9... . This notation is defined as meaning the limit as n approaches infinity of the sum from k=1 to n of 9/10^k . A sequence doesn'
by umanwizard 9y ago
There is such a thing as 0.9... .
This notation is defined as meaning the limit as n approaches infinity of the sum from k=1 to n of 9/10^k . A sequence doesn't have to reach its limit!! For example, the limit of the sequence 1/2, 1/4, 1/8, ... is 0, even though the sequence never reaches 0. The limit of the sequence 0.9, 0.99, 0.999, ... is 1 (and this is BY DEFINITION what 0.999... means).
- pacala 9y agoIn this Universe, no n has been observed to approach infinity.
- marcosdumay 9y agoIn this Universe, numbers do no exist, operations on quantities are meaningless, and things are not something. Or, you can decide to give some arbitrary meaning to all that stuff, and get some incredibly useful results. It's your choice.
- umanwizard 9y agoMath isn't directly about the concrete universe; it's an abstraction.