Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 4   Last Post: Oct 4, 2017 4:05 PM

 Messages: [ Previous | Next ]
 FromTheRafters Posts: 248 Registered: 12/20/15
Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted: Oct 4, 2017 7:43 AM

netzweltler was thinking very hard :
> Am Mittwoch, 4. Oktober 2017 11:44:35 UTC+2 schrieb Zelos Malum:
>>> In fact it means exactly infinitely many commands.
>>> But of course if you define a series to be equal to its limit, then that's
>>> like defining an apple equal to an orange. That is your problem, not ours.

>>
>> It doesn't because it is not operations upon operations, it is just a
>> representation of one element in real numbers.

>
> It does. And 0.875 is representing 3 operations, e.g.
> 0.8 + 0.07 + 0.005 or
> 0.5 + 0.25 + 0.125.
>
> It can be an element AND represent some number of operations.

I agree. The thing is that a finite number of steps (or commands) can,
at best, give a good enough approximation of some numbers. By adding
'ad infinitum' to the 'end' of these, and assuming it can be completed
in that (NaN) number of steps, you can arrive at the exact answer. This
is a case where it is not about the trip, but about the (eventual)
destination being defined exactly.

As you already know, an arrow traveling from zero toward a target at
two which can be described as going halfway there then halfway the
remaining distance, then halfway again, may seem like an unending
process with only better and better approximations being attainable.
But, if I can get that same step by step process by stating that the
process is actually pulling the arrow half the distance (from zero to
two for example) then I don't need the unending process anymore as I
already have the destination and the fact that the process is the same
confirms that two is the answer I want.

Insisting on the process while standing two units in front of the
archer will not save you from getting the point. :)

Date Subject Author
10/4/17 zelos.malum@gmail.com
10/4/17 netzweltler
10/4/17 FromTheRafters
10/4/17 netzweltler