Re: infinity

"David R Tribble" <david@xxxxxxxxxxx> writes:

> Virgil said:
>>> Since 'sequence' implies that each item in the sequence is
>>> followed by a unique 'next' item, can TO imagine what is the
>>> unique 'next' item after '0'?
>>
>
> Tony Orlow wrote:
>>> 0.000...000:000...000:::000...000:000...001!
>>>
>>> There you are: N^-N. The exclamation point can be for emphasis, but
>>> I am rather considering it as a candidate symbol to mean that we
>>> have gotten down to the level of the continuum and can go no
>>> further. So, there's you indivisible infinitesimal, one point away
>>> from 0. It's sort of like some people's 1- 0.999...
>>
>
> imaginatorium writes:
>>> OK, do your "real numbers" form a field? (You don't know anything
>>> about algebra, I know, so I'll help you: the real mathematical reals
>>> do, and it means you can always divide, subtract, etc. It implies
>>> that for any two distinct reals a and b you can calculate
>>> (a+b)/2. So if a=0, and b=your monstrosity above, what is (a+b)/2?
>>
>
> David Kastrup wrote:
>> No, it does not imply that. Z/2 is a field, and (a+b)/2 does not in
>> general exist in it.
>
> But surely R/2 is a field, and (a+b)/2 does exist in it, right?

Uh, R/2 is a field? With what arithmetic?

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

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