Re: Well Ordering the Reals

David R Tribble said:
>> At any rate, we could try a similar (but different) addition using
>> your notation (where c and d are not the same as a and b above):
>> c = 0:101010...101010
>> d = 0:110110...110110
>> + ------------------
>> s = 0:1000000...000000
>>
>> Hmm. It looks like s is one bit longer than c and d, even though
>> they are all (supposedly) infinitely long numbers. Or perhaps
>> we've simply just run out of bits, even though each number has an
>> infinite supply of them?
>

Tony Orlow wrote:
> So what? There are larger infinities and smaller infinities. Haven't I been
> consistent in saying even one bit makes a difference to an infinity, and even
> one additional element? When you add two digital numbers of a given length,
> what are the chances that the sum will be one bit longer? about 50/50. What's
> wrong with that? Does it work TOO much like finite math for you?

The "in-" of "in-finite" doesn't mean anything to you, does it?
It's pretty clear, at least to most of us, that "infinite" means
"not finite", and thus that "rules of finites" are not the same as
"rules of infinites". But you don't get that.

When you say a number like x = 1:1010...1010 has N digits,
where N is supposedly infinite, this means that 2x has N+1
digits and x^2 has 2N digits, etc. What good is N for, then?
It's completely arbitrary and essentially meaningless, since it
doesn't really tell us anything useful about infinite numbers.
N might just as well be finite, for all the good it does you.
And indeed, that's how you treat it.

But that simply reflects your whole problem with standard math.
You don't really seem capable of comprehending what "infinite"
really means. Oh sure, you say things like "never ending", and
"continues forever", and "unending supply", which implies that
you might just get it. But then everything else you say makes it
obvious that infinity is just a really big finite number to you.
I can only conclude that, as bright as you seem to be, you
cannot concieve of anything being truly infinite.

.

Relevant Pages

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