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> if you were doubtful that 0.999... = 1, then you should also be doubtful that 0.333.. = 1/3 I disagree. Any middle school student can calculate 1/3 to be 0.3
by notRobot 7y ago
> if you were doubtful that 0.999... = 1, then you should also be doubtful that 0.333.. = 1/3
I disagree. Any middle school student can calculate 1/3 to be 0.33333... using long division, but there's no immediately obvious way to go from 1 (or 1/1) to 0.9999...
- The_Colonel 7y ago> Any middle school student can calculate 1/3 to be 0.33333... I can just do it backwards - is 1/3 equal to 0.33333...? 1 / 3 = 0.33333... 3 * 0.33333... = 0.99999... and my child brain "knows" that 1 != 0.99999... In my child brain this proves that 1 / 3 is not equal to 0.33333..., it's just an approximation. So I agree with larschdk, those problems are equivalent and one can't be used to prove the other ...
- ant6n 7y ago> Any middle school student can calculate 1/3 to be 0.33333... using long division, ... ...the same way That Chuck Norris can count to infinity... twice!
- mywittyname 7y agoI smart middle-schooler is absolutely capable of understanding that dividing 1/3 results in an infinitely repeating sequence of 0.33333... Even without understanding the concept of infinity, they will quickly realize that there's no reason to believe the problem will stop adding a 3 to the end of the result with each iteration.
- ant6n 7y ago> I smart middle-schooler is absolutely capable of understanding that dividing 1/3 results in an infinitely repeating sequence of 0.33333.. And how will I smart middle-schooler know that the result of running the long division algorithm is exactly 1/3, rather than some approximation.
- gbrown 7y agoRecursively?