Mageth

Photocrat:

*ahem* That doesn't show .99999... = 1.

You guys need to read up on set theory. I agree that some of it is counter-intuitive, but it is legitimate mathematics.

Yes, .999999[repeating] *is* equal to 1. Or are you saying that you don't believe limits "really" converge?


Well, if that's what you're getting at, then why didn't you just come out and say so, instead of using that rather deceitful little algebra trick, dropping the "x" from the 9? My answer is valid if viewed as a simple problem in algebra, which is how you stated it. If you're so good at set theory and mathematics, why resort to trickery and deception? It appears to be that your purpose was to trick and embarass those not as "smart" as you, something I got over in grade school. "I know set theory and you do not, na na na na naaaa na."

Apikorus

Try this:

• x = 0.99999...
• 10x = 9.99999... = 9 + 0.99999... = 9 + x
• 10x - x = 9
• 9x = 9
• x = 1

HRG

[quote]Originally posted by daemon23:
[QB]My question was not an attempt to correct, but a question of validity--is (10 * 0.999...) truly equivalent to 9.999...?
[quote]
Yes. Infinite decimal fractions are convergent series; multiplication with a constant and passage to the limit commute.

According to mathematical notation, those two expressions mean exactly the same thing.

Regards,
HRG.

HRG

Or:

1 - 1 + 1 - 1 + .... = (1-1) + (1-1) + ... =
0 + 0 + ... = 0

But:

1 - 1 + 1 - 1 + ..... = 1 - (1-1) - (1-1) - .... =
1 - 0 - 0 - .... = 1

And:
1 - x + x^2 - x^3 + ... = 1/(1+x); let x=1:

1 - 1 + 1 - 1 + 1 + .... = 1/(1+1) = 1/2.

Since we have started each time with the same infinite series, we have shown that 1 = 0 = 1/2.

Regards,
HRG.

Bill Snedden

But equivocations do not correct answers make...

Nice example, only...

It has nothing to do with the question you asked. To begin, your answer assumes a cube or some other 3-dimensional parallelogram, not a square. But to the point, "the shadow of a spinning square" is not "a square". The appearance of a circular shadow is caused by a trick of optics as some of the light will be deflected from following the object's true boundaries by its rotation; in essence, an optical illusion. This would be true in either 2 or 3 dimensions, so the "Flatland" reference would seem to be a non-sequitur.

Same answer as above. Perhaps if you had phrased the questions more accurately, say, "How can a square appear to be a circle?", or "When does a triangle appear to be a circle?"

Is that perhaps your point? That God only appears to be a trinity, but is actually a unity? Or that the trinity is some form of optical illusion?

At any rate, your equivocative answers clearly do not match the questions you posted. Squares and triangles cannot actually be circles, as anyone who's taken elementary geometry can no doubt inform you.

From my reading, electrons are not both particles and waves at the same time and the same place, they merely exhibit the behaviors of both at different times.

In other words, sometimes when you look at an electron it appears to function as a particle; other times it appears to function as a wave.

Again, by analogy are you saying that sometimes God appears to function as the Holy Spirit and sometimes He appears to function as Jesus? That he isn't really either one, but just seems to be? That's an interesting idea, but doesn't seem to fit with any Christian doctrine of which I'm aware.

Hmmm..I don't see anything in QM, at least so far as you've shown & from what I've read, that justifies that conclusion.

Hmmmm again....

Analogy: resemblance in some particulars between things otherwise unlike.

Your "analogy" does not appear to meet the accepted definition of the term. Perhaps you left some parts out?

Basically all you did was assert that God was beyond our understanding and then use that assertion to justify the self-contradictory definition of the trinity. As that's the very thing under discussion, this amounts to no more than question-begging.

I can definitely go along with that. The more I learn, the more I realize just how much I don't know...

James Burke's "Connections" used to be a regular feature in "Scientific American", but it looks like they removed it recently. I will miss it.

I would very much have liked to see the end, but unfortunately, no one has as of yet been able to offer a coherent description of it. And so, for now I must of needs continue my voyage...

Regards,

Bill Snedden

Photocrat

Eh? That wasn't a trick, it's just counter-intuitive. You assume that there's a "last" number there when you say that it should end with zero--there isn't one, it's an infinite series. Let's try this another way --

.999_ = .888_ + .111 [no objection here, right?]
.888_ = 8/9 [check by long division--there are *no* 9s at the 'end', your calculator may round it for you, but it doesn't end, as you can see from long division]
.111_ = 1/9 [same as above]
.999 = .888_ + .111_ = 8/9 + 1/9 = 9/9 = 1
QED

I don't mean to be snotty & say "hahaha, I know more than you do" -- I appologize for coming off that way.

OTOH, I object to the 'you idiots, 1 != 3!' nonsense we have to put up with, which started my little rant.

I mean, I feel the way skeptics probably do when fundamentalists dont' believe them about evolution right now... [I happen to think it's valid science, but I digress]

In any event, there's at least one skeptic here who *does* appreciate this math--HRG [thanks!] Ask him if you still don't believe me. He's one of the nicest skeptics I've met, not to mention one of the smartest :] He's pretty good at QM, too--quite a bit more than the common "oooh! I just learned about the uncertainty principle!" chatter :]

Photocrat

Even you have 9.99999... = 9x + x, so I don't see the complaint? If you believe in a '.000...1' being left off, you've just left off a bunch of them? To worry about the 'last' digit implies that there is one; which is contrary to the statement that it is a repeating decimal... one which repeats *without end* ...

I'm sure that ambiguous decimal expansions aren't something they teach most people about, though ...

To make a long story short, if you assert otherwise, you assert a contradiction (it both has & doesn't have an end??? I said it didn't & then you assumed it did...) which only proves me correct [proof by contradiction] ...

Photocrat

If you take 'infinite' to be something like 'set of all sets', of course it's a contradiction. However, there are other senses of the word 'infinite' which make more sense. For example, the rational numbers are a subset of the real numbers, so you could have the set of all rational numbers and still 'exist outside that', in the real numbers... There are other analogies to use, which might better approximate how you think God would exist in relation to the world if God existed; but I think I'm having enough trouble conveying simpler things to leave it at that :] Besides, you might give the names of the sets I would use as examples a bit more theological import than they require as analogies...

Yeah, I know that mathematical analogies are going a bit overboard by now, but the root problem here is being informal about the terminology :] The same ambiguity, which most people don't realize is there, is why my explanation of ambiguous decimal expansions went so badly...

Suffice it to say, there are many definitions of 'infinte' which do not lead to contradictions of the sort you're thinking of, which can be employed to describe God & still leave us with something other than pantheism :]

Photocrat

You should've told them that:

1 + (2 - 2 + 2 - 2 + ...) = 1 + (0 + 0 + ...) = 1

and

1 + (2 - 2 + 2 - 2 + .....) = 1 + (2 - (2-2) - (2-2) - ....) = 1 + (2 - 0 - 0 - ....) = 3

so we'd have '1 = 3' :]

daemon

Okay, then I stand corrected. Not much call for knowing advanced algebra in programming, thankfully...