you: They certainly do. That is why your sources are questionable to me, even if they come from "the Math whiz" himself. Two parallel lines are no longer "parallel lines" if they intersect. By definition, they are NOT parallel. To BE a parallel line, it must NOT intersect. If it intersects, it is no longer a parallel set of lines. My objections remain.
Having said that, mathematics is unreasonably effective in the natural sciences.
Indeed, I often point to the unreasonable effectiveness of math as God's copyright notice on the cosmos.
Reimannian Geometry is an excellent example. It was developed in theory long before Einstein came along and pulled it off the shelf to describe General Relativity.
The mathematics, the logic, the language is writ large across that part of God's Creation we can physically observe.
The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. [There is] no speech nor language, [where] their voice is not heard. – Psalms 19:1-3
But physical reality is not infinite. It is very much finite and thus such concepts as parallel lines if visualized in the physical sense, would not intersect. But in math theory, they do ... at the point in infinity. Think about it.
Of course God is not subject to time or space. He created them! His Name is I AM.
That is why I aver that “timeless” is a better adjective than “eternal” when speaking of God the Creator of “all that there is” whether spiritual or physical - including time!
But God’s Names are also Alpha and Omega – and Immanuel.
And as Dr. Eckleburg has pointed out, the Holy Spirit indwells us mere mortal denizens of space/time.
I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me. – Galatians 2:20
One also then realizes His Names Alpha and Omega point to the First Cause and the Final Cause of “all that there is” – namely, Jesus Christ Himself:
As to points on a line and infinity, please explain to me how two points on an infinite line are distinct from each other. How is one closer to another point when there is no minimum or maximum?
Infinity is not "no quantity" like you are using it. No quantity would be "null" - not zero, but null - void, empty.
The “Line at Infinity” is the straight line on which all “Points at Infinity” lie. Mathworld
And any number sequence, e.g. -3, -2, -1, 0, 1, 2, 3 – can be extended or projected, in either a positive or negative direction to infinity, i.e. an unbounded quantity greater than every real number.
Moreover, from Aristotle, the concept of “time” comes from counting … 1, 2, 3.
Eternity is not “no time” or “timelessness” it is “time without end” – or as the Epistle of Barnabas put it, a time of not counting.
If it were “no time” or “timelessness” then it would be the ex nihilo - void, null, empty – which preceded God’s Creation of “all that there is” – both spiritual and physical.
The Father is not begotten. Jesus Christ is begotten of the Father. The Spirit is from the Father by the Son.
For unto which of the angels said he at any time, Thou art my Son, this day have I begotten thee? And again, I will be to him a Father, and he shall be to me a Son?
And again, when he bringeth in the firstbegotten into the world, he saith, And let all the angels of God worship him. And of the angels he saith, Who maketh his angels spirits, and his ministers a flame of fire. But unto the Son [he saith], Thy throne, O God, [is] for ever and ever: a sceptre of righteousness [is] the sceptre of thy kingdom. – Hebrews 1:1-8
To God be the glory!
Having said that, mathematics is unreasonably effective in the natural sciences
There is nothing unreasonable about mathematics. They are effective in natural sciences to the extent that they mathematics allows for working models. Working models prove nothing, They just work. Thye do not necessarily represent truth or "reality."
Infinity is an unbounded quantity greater than every real number Mathworld
In your previous post you defined infinity as bound by time and space.
And any number sequence, e.g. -3, -2, -1, 0, 1, 2, 3 – can be extended or projected, in either a positive or negative direction to infinity, i.e. an unbounded quantity greater than every real number
So what? Besides, positive and negative directions is irrelevant in infinity.
I am not sure what is the point you are trying to make. Can you reduce it to a single sentence or at least a paragraph?
I think logically. The term "parallel lines" has a definition. If this definition is violated, it no longer IS a parallel line that we are discussing, but something else. If you have a triangle, and add another side to it, does it remain a triangle? Such speculations is nonsense to my mind. Parallel lines that intersect are not parallel lines anymore.
And at WHICH point would these "parallel lines" intersect at? If you distinguish between two points in infinity, you have destroyed the definition of eternity! As you note elsewhere, and perhaps do not realize it, the “Line at Infinity” is the straight line on which all “Points at Infinity” lie. I agree, and have said as such. ALL points on an infinite line are the same. Thus, if you distinguish between two points, say one that intersection occurs and one point where intersection does NOT occur at, you have distinguished and ruined your definition.
I wrote: My point is that God is not subject to time. Thus, the idea that "eternity is time without end" is an incorrect definition.
You replied: The second statement does not follow from the first. Of course God is not subject to time or space. He created them! His Name is I AM. That is why I aver that “timeless” is a better adjective than “eternal” when speaking of God the Creator of “all that there is” whether spiritual or physical - including time!
You seem to contradict yourself. First, you say that eternity is "time without end", which I say is incorrect, then you talk about "timeless as being a better adjective. Are you still in the midst of thinking out loud and trying to determine your point of view?
"Timelessness" means no time. Not "time without end". "Eternity" does NOT have a beginning. "Time without end" DOES! Thus, you are incorrect, as I have said before. Eternity and time without end are not the same thing.
Infinity is an unbounded quantity greater than every real number
I disagree. Infinity has no "quantity" because there is no distinction. Minimum and maximum are IDENTICAL! There is absolutely NO distinction in infinity. You have already admitted as such when you say "all points on an infinite line are the same". Infinity is not "one plus the last number"!
Eternity is not “no time” or “timelessness” it is “time without end” – or as the Epistle of Barnabas put it, a time of not counting.
I have already addressed this error. "time without end" is only projected in one direction. Eternity is without end in EITHER direction. Thus, there is no future or past in eternity. In "time without end", we realize that time has a starting point, but without end. That is TWO DIFFERENT things, A-G. I suggest you read Nicholas of Cusa and "On Learned Ignorance"
If it were “no time” or “timelessness” then it would be the ex nihilo - void, null, empty – which preceded God’s Creation of “all that there is” – both spiritual and physical.
That is revelation. "Before" God created time, there was nothing. We believe God created from nothing.
The Father is not begotten. Jesus Christ is begotten of the Father. The Spirit is from the Father by the Son.
"the Spirit PROCEEDS from the Father THROUGH the Son". The Father is the principle of the Spirit. Kosta, anything to add? Otherwise, you have expressed the catholic/orthodox trinitarian belief.
Regards