Mageth

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

No problem and sorry I jumped on you. I consulted with my more mathematically-versed friends at work and they both backed you up. BTW, I have little problem understanding convergence of infinite series. After a little discussion and some alternative formulations, I've overcome, and retract, the counterintuitive objection I posed to your example.

One formulation I did that helped me was taking out the x (and subbing 2 for 10 to show a different case):

2(0.999...)=1.999...
2(0.999...)-0.999...=(1.0+0.999...)-0.999...
0.999...=1.0

Since we know by convergence of infinite series that 0.999...=1, this seems more intuitive to me.

Tercel

Ah the many joys of illegal maths... Can I play?

Let x = 0
4x = 2x (since both sides are zero)
4x - x = 2x - x (subtract x from both sides)
x(4-1) = x(2-1) (factorise)
4-1 = 2-1 (divide both sides by x)
3 = 1 (simplify)
QED

(-1)^3 = -1 (ie -1 cubed is -1)
(-1)^6 = 1 (square both sides)
((-1)^3)^2 = 1 (factorise the power term)
(-1)^3 = 1 (square-root both sides)
-1 = 1 (simplify the LHS)
1 = 3 (add 2 to both sides)
QED


Okay apart from that, since it has taken three pages for no one to explain the Trinity properly, (I note there have been a couple of half-hearted attempts by Photo and Theo) so I might as well waste my time explaining...
I think the trinity is best viewed using the Greek analogy Photo brought up:
In Classical Greek plays there were only 2 to 4 different actors, despite the fact that there were more parts than that in the play. Thus, throughout the play, each actor would normally play several different characters. Including costuming etc, each character in the play always had a different face mask and the actor would, once off-stage, change their mask to completely look the part of the new character. Each of these characters in the Greek plays was called a Persona. We derive our word "Personality" from this Greek root - and of course each character or Persona in the play had a different personality, as well as looking physically different because of costuming, masks etc.
So how does this relate to the trinity? The doctrine of the trinity is about having 3 Persona in one Essence. Like a Greek actor would take on 3 different Persona in a play while remaining one thing, so God takes on three different Persons while remaining one Essence.
Perhaps the best way to fully understand it, is to look at the heretical extremes, see why they are wrong, and deduce the correct understanding:
Now one extreme is Modalism, (see Theo's accusation in his post above) which says that God is simply one being which we perceive as 3: In reality God is completely and utterly one Person, it is simply an illusion of our perspective that happens to make it look like to us that he is 3 different beings - that's simply the way we perceive him similar to mistaking a person's front, side and back for three different beings. Now, Modalism differs from orthodoxy in that it plays down too far the real nature of the Trinity. Orthodoxy asserts that we perceive God as three different beings because He does have three different persons which are actually different to one another and not simply different ways of looking at the same thing.
The other extreme is Tri-Theism, which says that the Trinity is simply three completely separate Gods. They are all Gods in their own right, and they work together often, but that's it. There is no ultimate unity between them any more than there is ultimate unity between you and me. In reality, Tri-Theists tend to degrade the status of the Jesus and the Spirit to a significantly lower status than that of the Father resulting in Arianism - basically denying the God status of Jesus and making him something less than God. (Usually still "divine" though in a lesser sense) Orthodoxy however asserts that fundamentally the Trinity is of one nature - just as fundamentally the 3 Persona in the play are played by the one actor.
Orthodoxy makes a distinction between Person (Personality, attributes etc) and essence (What it truely is and is made of at a fundamental level): 3 Persons, one Essence (aka Substance aka Godhead).

The Ecumenical Athanasian creed (written against the Arians) gives the most complete statement on the trinity from the orthodox view, so I will examine the relevent parts of that (Creed in bold):
<strong>We worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons, nor dividing the Substance. For there is one Person of the Father, another of the Son, and another of the Holy Ghost.</strong>
The 3 persons are separate and should not be thought of as only one ("confounded"), nor should the fundamental substance of God be split up like Tri-theism.
<strong>But the Godhead of the Father, of the Son, and of the Holy Ghost is all one: the glory equal, the majesty coeternal. Such as the Father is, such is the Son, and such is the Holy Ghost. The Father uncreate, the Son uncreate, and the Holy Ghost uncreate. The Father incomprehensible, the Son incomprehensible, and the Holy Ghost incomprehensible. The Father eternal, the Son eternal, and the Holy Ghost eternal.</strong>
All three persons are equally glorious, uncreated, incomprehensible and eternal.
<strong>And yet they are not three Eternals, but one Eternal. As there are not three Uncreated nor three Incomprehensibles, but one Uncreated and one Incomprehensible. So likewise the Father is almighty, the Son almighty, and the Holy Ghost almighty. And yet they are not three Almighties, but one Almighty. So the Father is God, the Son is God, and the Holy Ghost is God. And yet they are not three Gods, but one God. So likewise the Father is Lord, the Son Lord, and the Holy Ghost Lord. And yet not three Lords, but one Lord.</strong>
Yet all three persons are ultimately one in being, so it is true to say that each one is Almighty, yet it is not true to say that there are three Almighties etc.
<strong>As Christian truth compels us to acknowledge each distinct person as God and Lord, so catholic religion forbids us to say that there are three gods or lords.</strong>
("catholic religion" being the orthodox Christian faith at the time of writing of this creed)
<strong>The Father is made of none: neither created nor begotten. The Son is of the Father alone; not made, nor created, but begotten. The Holy Ghost is of the Father and of the Son: neither made, nor created, nor begotten, but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. </strong>
This is the way in which the three persons are related to each other. The Son is not a created being, but rather he is "begotten" (born) of the same substance as the Father. The Spirit "proceeds" from the Father and the Son.
<strong>And in this Trinity none is before or after other; none is greater or less than another; But the whole three Persons are coeternal together, and coequal: so that in all things, as is aforesaid, the Unity in Trinity and the Trinity in Unity is to be worshiped...</strong>
The Persons are entirely equal in status to one another, and they are ultimately "together" or united eternally.
<strong>...Lord Jesus Christ, the Son of God, is God and Man; God of the Substance of the Father, begotten before the worlds; and Man of the substance of His mother, born in the world; Perfect God and perfect Man, of a reasonable soul and human flesh subsisting. Equal to the Father as touching His Godhead, and inferior to the Father as touching His manhood; Who, although He be God and Man, yet He is not two, but one Christ: One, not by conversion of the Godhead into flesh, but by taking the manhood into God; One altogether; not by confusion of Substance, but by unity of Person. For as the reasonable soul and flesh is one man, so God and Man is one Christ....</strong>
Just as a mind in a human body is one man, so the Christ the 2nd person of the Trinity in the body of a man was only one: not Christ the spirit and Christ the body (as was mentioned earlier on this thread).

Tercel

Bill Snedden

It actually took me about two minutes of thinking, "what the hell...?" before I realized why this WAS "illegal"...

It's been way too long of a day.......

But seriously: Tercel that was a noble effort...

However, explaining that a proper conception of the trinity lies somewhere between modalism and tri-theism really doesn't help explain what it is (and did you really have to post the whole long-ass Athanasian creed? When I first saw that thing in my BCP, I wondered if it had been created as a "method" of the inquisition. "Now, repeat after me.. &lt;drone, drone...&gt;" "AAAGH! I confess!" ).

I'm sure that we were all taught pretty much the same thing: can't explain it, it's a mystery, etc (of course, being raised Catholic, I also had St. Patrick's shamrock example ). That's the point of the thread, though. Within the context of faith, mystery is a justified "retreat" when fallible human knowledge fails (and I don't mean that perjoratively).

However, in the course of witnessing, how does a believer expect to be able to explain to a non-believer a concept that he himself cannot grasp or articulate? Why should any non-believer be expected to accept on faith anything that a believer cannot explain without resort to that very faith that is the matter in question?

Kind of a tough row to hoe, wouldn't you say?

Now, as I know that theophilus harks from a reformed or Calvinist tradition, I pretty much already know his answer to this. I'm more interested in hearing from those Christians whose doctrine doesn't completely rob the Great Commission of all meaning. How does one "spread the gospel" if one can't even articulate its basic concepts?

Regards,

Bill Snedden

[ January 29, 2002: Message edited by: Bill Snedden ]</p>

CardinalMan

I think that all of the confusion about 1 = .999999... just validates why mathematicians do not define the real numbers in terms of infinite decimals, and do not allow the somewhat careless arguments employed above. You can not talk about convergence of an infinite series (the decimal expansion) to a real number before you have defined what a real number is (which to avoid circularity, can not involve decimal expansions). Unfortunately, very few nonmathematicians know how to do this, let alone that it has even been done. It wasn't until the end of the nineteenth century that Dedekind and Cantor came up with independent rigorous definitions of the real numbers (using Dedekind cuts and Cauchy sequences of rational numbers, which I will elaborate on if people are interested) to avoid these problems and give real numbers a sound formal existence.

So yes, 1 = .99999..., and the above arguments give intuitive ideas why you should believe this equation, but they are not mathematical proofs.

CardinalMan

Photocrat

Appology accepted. I, in turn, am sorry for seeming to be condescending in asserting myself.

Of course, it's true that, as CardinalMan has just pointed out for us, the real truth is just a tad more complicated... :] I could spell out a more full formulation, but it would be long & probably boring for most people... I mean, you don't usually think of a real number as the limit of a Cauchy sequence... Even so, with all our definitions, we can show that distinct sequences (.999..., 1.000...) can represent the same rational number, as I was pointing out :] Not very intiutive, is it?

Photocrat

Yes, but would you rather I give them a long lecture on set theory? The one where 8/9 + 1/9 = 1 is probably the best, but the minute I got to the equivalence of Cauchy sequences (& the null sequence, equivalence relations, sets... and all the other requirements), I would have bored people to tears...

lpetrich

This discussion reminds me of Gore Vidal's reference to the religion of "the crucified tripartite man-god".

As to wave-particle duality, that is abundantly verified experimentally, even though exactly why it happens is a murky question.

CardinalMan

Of course! Everyone needs more set theory in their lives.

But seriously, I did not mean that you should go into the (necessarily) technical deveopment of real numbers. I just wanted to point out that there are many things being swept under the rug, and that much of the confusion comes from the fact that nobody here has discussed what exactly a real number is (it is not an infinite decimal). Hence, for those people who are confused, know that you have good reason for being confused. Mathematicians grappled with these questions for centuries before providing a satisfactory foundation.

CardinalMan

sbaii

Your explanation of how a square becomes a circle is clever but there is a little deception involved. You start out using a three dimensional square to create the optical illusion of a cylinder. The resultant circles are two dimensional. The same goes for the triangle. The three dimensional square is actually a rectangular solid if I remember my h.s. geometry.Calling it such might have tipped Bill off if he is really into geometry. It wouldn't have helped me...And I don't see how it relates to the original question on the Trinity. OOOOO! I just hate smart-alecky tricks like that!

Mageth

I've thought about this and decided I have no problem with the triune god stuff. It's easy for 1=3:

God doesn't exist.
G = 0
Since god doesn't exist, he couldn't have a Son.
S=0
nor a "Holy" spirit
H=0

From the above:
G+S+H = 0+0+0 = 0 QED