Re: infinity

Tony Orlow (aeo6) wrote:
>> What consistency! What was the contradiction in the notion that [0,1) is
>> half the size of [0,2) again?
>
David R Tribble said:
>> If you're right, you should be able to name twice as many points
>> from [0,2) than I can name from [0,1).
>>
>> But while you can name two points in [0,2) for every point I choose
>> in [0,1), I can also name two points in [0,1) for every point you
>> choose in [0,2).
>>
>> b = a x 2, for all a in [0,1)
>> and b in [0,2)
>>
>> c = d / 2, for all d in [0,2)
>> and c in [0,1)
>
Tony Orlow (aeo6) wrote:
> Your mapping function demonstrates the ratio of 2 between these two sets of
> reals.

Well, it demonstrates the ratio between the numeric values of
corresponding members of the two sets.

It also demonstrates that the two sets have exactly the same number
of members; any given member of one set will have a numeric value
that is exactly twice or half of the corresponding member in the
other set.

Unless, of course, you can provide members of one set that don't
correspond to any members of the other set. Find a b that has
no corresponding a, or a d that has no c.

.

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