The OP is a summary of the sentiments I've gotten from Christians over the years. If you refuse to point out something that you dispute, you prove me right. It's only 4 lines of text.
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So you have no source for "Christians say..." I dispute that your OP represents what Christians think if you cannot provide a source. Carry on with your strawman, though.
The dirty truth of mathematics is that it is nothing but assumptions, definitions, and the conclusions that follow. The assumptions are typically referred to as axioms or postulates. This relates to the Münchhausen trilemma and nihilism.
That is very interesting. I suppose the bijection only exists in the case where n is infinite, because there are about twice as many elements in Z as there are in N when n is finite? That's very strange and makes me think it might be important at times in physics and astronomy to know if things are truly infinite or merely unfathomably large. I guess space is believed to be finite, but there is an assumption that an infinite number of coordinates exist in space - much as an infinite number of real numbers exist on a finite line segment. Maybe it doesn't matter. I saw an old lecture on youtube where Richard Feynman mentioned a student's concern that the universe might be discrete rather than continuous. Feynman had some seemingly simple argument for things being continuous, but I couldn't follow it.Well... N and Z are actually the same size, even though N is a proper subset of Z. So even though {0,1,2,3,...} is fully contained in {...,-3,-2,-1,0,1,2,3,...}, there exists a bijection between them (a one-to-one mapping which goes both ways). For example, take f:N→Z such that f(0)=0, f(2n)=n, and f(2n-1)=-n for n>0.
Feynman had some seemingly simple argument for things being continuous, but I couldn't follow it.
That is very interesting. I suppose the bijection only exists in the case where n is infinite, because there are about twice as many elements in Z as there are in N when n is finite?
That's very strange and makes me think it might be important at times in physics and astronomy to know if things are truly infinite or merely unfathomably large. I guess space is believed to be finite, but there is an assumption that an infinite number of coordinates exist in space - much as an infinite number of real numbers exist on a finite line segment.
Maybe it doesn't matter. I saw an old lecture on youtube where Richard Feynman mentioned a student's concern that the universe might be discrete rather than continuous. Feynman had some seemingly simple argument for things being continuous, but I couldn't follow it.
I hate to even ask, but is the number of rational numbers the same as the number of natural numbers? LOL
Something starting without a cause is not logical nor consistent unless you can explain how that would happen or where that has ever happened.Unless there’s an exception in which some beginnings don’t have causes. You’re postulating that something might exist which never began to exist. An alternative exception to invent is that something may have begun to exist without a cause. What makes your exception more valid?
Neither is something existing without having begun to exist.Something starting without a cause is not logical nor consistent unless you can explain how that would happen or where that has ever happened.
Now if that were true nothing would exist.Neither is something existing without having begun to exist.
That doesn’t follow. You are simply more comfortable with something existing without a beginning than something beginning without a cause. Neither has been empirically observed, so why believe in one over the other?Now if that were true nothing would exist.
What is the cause of everything that exists?That doesn’t follow. You are simply more comfortable with something existing without a beginning than something beginning without a cause. Neither has been empirically observed, so why believe in one over the other?
And yet in-order to force doubt upon (at least some) of these fundamental tautologies, one must necessarily behave irrationally.
Atheists claim to value reason. So then why do they tend to abandon reason when it gets down to the level of axioms? Because it gets uncomfortably close to proof of God, so they necessarily must abandon reason in-order to force their incredulity. IOW, a much higher priority is revealed, and that's a personal will to suppress reason, and not reason itself.
What I've disputed and has been proven is a baseless and unattributed assertion made by you, since you cannot back it up. The Bible says no such thing to support to your poorly constructed OP, so you'd have to demonstrate from somewhere else that it is a Christian position held outside of a few "Christian" interactions you've had over time. Is there a Christian denomination that agrees with your OP? A Christian theologian? Someone other than anonymous Christians to support your "Christians say.."?The OP is a summary of the sentiments I've gotten from Christians over the years. If you refuse to point out something that you dispute, you prove me right. It's only 4 lines of text.
What I've disputed and has been proven is a baseless and unattributed assertion made by you, since you cannot back it up. The Bible says no such thing to support to your poorly constructed OP, so you'd have to demonstrate from somewhere else that it is a Christian position held outside of a few "Christian" interactions you've had over time. Is there a Christian denomination that agrees with your OP? A Christian theologian? Someone other than anonymous Christians to support your "Christians say.."?
That's interesting to read about Hilbert's Hotel. Very weird.N and Z are infinite sets by definition. N is not something like {0,1,2,3,...,n}. But to answer what I think you're asking, yes, if A is a proper subset of B and if there exists a bijection between A and B, then both A and B must be infinite. Formally, a set X is infinite if there exists a function f:X→X such that f is injective but not surjective. More fancy words but basically it's illustrated by Hilbert's Hotel.
I don't think this is the prevailing notion. The observable universe is certainly finite as it is a sphere whose radius is a function of the age of the universe. But the actual universe is presumably strictly larger than the observable universe and is potentially infinite. As for coordinates of the universe, there is no sensible way of describing this as being infinite because there is nothing discernible about what occurs on the Planck scale. We could partition the current observable universe into finitely many Planck cubes.
Interesting. I'm not going to dispute anything Feynman has stated but to my knowledge we cannot comment on the nature of space beyond the Planck scale.
Yes, there exists a bijection between the rational numbers and the integers. However, the set of real numbers is "more numerous" than the set of rational numbers. There is no bijection that exists between Q and R, and this fact has generated hierarchies of infinities. The size of Q, denoted |Q|, is the smallest infinity, and the size of R is strictly larger. It is unknown if there exists X such that |Q|<|X|<|R|. This is the continuum problem. See Cantor's diagonalization argument for the proof that |R|>|Q|.
Why assume that there must be one?
Then your knowledge is lacking. As is your "source". And now you're just being dishonest, saying that I agree with you. It's your thread, devolve it as you wish.To my knowledge, every Christian denomination agrees with my position, as does every Christian, including you.
What about the Nicene Creed which is the definition of "Christian" at CF? This seems to match what @Nihilist Virus expressed as the common view of Christians. I grew up in the Episcopal Church and the OP matches what I believed. I don't doubt that there might be some theologians with a different view, but I think it is fairly typical for laypeople to believe that.What I've disputed and has been proven is a baseless and unattributed assertion made by you, since you cannot back it up. The Bible says no such thing to support to your poorly constructed OP, so you'd have to demonstrate from somewhere else that it is a Christian position held outside of a few "Christian" interactions you've had over time. Is there a Christian denomination that agrees with your OP? A Christian theologian? Someone other than anonymous Christians to support your "Christians say.."?
English versions of the Nicene Creed - WikipediaI believe in one God,
the Father Almighty,
maker of heaven and earth,
and of all things visible and invisible;
And in one Lord Jesus Christ,
the Only Begotten Son of God,
begotten of his Father before all worlds,
God of God, Light of Light,
very God of very God,
begotten, not made,
being of one substance with the Father;
by whom all things were made;
who for us men and for our salvation
came down from heaven,
and was incarnate by the Holy Ghost of the Virgin Mary,
and was made man;
and was crucified also for us under Pontius Pilate;
he suffered and was buried;
and the third day he rose again according to the Scriptures,
and ascended into heaven,
and sitteth on the right hand of the Father;
and he shall come again, with glory,
to judge both the quick and the dead;
whose kingdom shall have no end.
And I believe in the Holy Ghost the Lord, the Giver of Life,
who proceedeth from the Father and the Son;
who with the Father and the Son together is worshipped
and glorified;
who spake by the Prophets.
And I believe one holy Catholic and Apostolic Church;
I acknowledge one Baptism for the remission of sins;
and I look for the resurrection of the dead,
and the life of the world to come. Amen
At one time we were not sure if the laws of logic applied to outer space, but we assumed they did and it turned out we were right. It is more rational to assume that logic is universally valid until proven wrong then not to, otherwise progress will never occur.Causality is a process within the universe. I'm not sure why you think this process extends beyond the universe. You're saying that the laws of the universe apply outside of the universe. That is not a reasonable position.
To my knowledge, every Christian denomination agrees with my position, as does every Christian, including you.
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