Re:0.999...= 1
by The_Colonel on Tuesday April 28, 2020 @04:31AM
(#23004928)
> 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 ...
> 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!
Re:0.999...= 1
by mywittyname on Tuesday April 28, 2020 @10:27AM
(#23007279)
I 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.
> 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.
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...