thomaq

how can you get infinitely close to something? i dont think this is possible by definition. infinite means non-ending, or non limited, and therefore incomplete. so to speak of something as BEING infinitely close, arent you attributing completeness to it? wouldn't it be more accurate to say, "getting infinitely closer"? but if you do this, then you can never speak of something in the past that was "infinitely close" to something. you can maybe say that something was GETTING infinitely closer and then changed direction or something.

what made me think of this is somewhere in this forum, (talking about cosmology and the big bang) someone brought up something being infinitely close to zero.

maybe i'm trippin? any thoughts?

Hawkingfan

Although I have not studied calculus formally, infinite numbers in calculus are numbers that grow and don't stop, no? At least in infinite limits. So you could have the number 0.01 and then 0.001 and then 0.0001 and so on forever but never reach zero.

SlateGreySky

So, it would seem that "infinitely close" is a vectorial expression rather than an expression of some scalar quantity. That is to say, whatever is "infinitely close" is constantly on the move, so to speak, in the direction of that to which it is infinitely close (in this case, zero).

thomaq

yes. and so it makes no sense to refer to something as having been infinitely close to something.

along these same lines, does it make any sense to say that something is, or ever has been, infinitely dense? this doesnt seem to make any sense at all.

Hawkingfan

But I thought you said in the OP that what was in question was something infinitely close to zero, which makes perfect sense.

And in calculus, can't a function on a graph approach horizontal and vertical asymptotes but never actually touch them...and result in limits involving infinity?

thomaq

i must say i am ignorant when it comes to calculus. i do agree that something can approach something and not touch it, but it cannot BE infinitely close. nor could something ever HAVE BEEN infinitely close. like i said, i am ignorant of calculus, so if i am missing your point or over-simplifying, i thank you in advance for your patience.

xoc

Not to but in, but I do believe h-fan was agreeing with the comment you made in the first post:

This referring to a series, described as getting closer to something infinitely(an infinite series) as you never reach zero.
1, .5, .25, .125, etc.
I don't even know enough about calculus to give the correct formula for this, but it is an infinite number of numbers before zero is reached on that one.

I don't think it makes sense to say you can be "infinitely close" to something unless (perhaps) the thing you are close to is "yourself"... but then again this is probably better understood as "absolutely close." point a is absolutely close to itself. Perhaps it could be said to be infinitely close, this is a bizzarre idea but it may make sense as you can definitely say the closeness between an object and "itself" is limitless(infinite) as there is no limit to it by definition. However this may not really be saying much, just some fun semantics.

xoc

To further my point a bit:

We speak of close and distant as relative terms to measure distance qualitatively. What is "close" or "distant" is a matter of opinion. However one is clearly the negation of the other.

We measure space(quantitatively) in "distance", not closeness. However the two are recipricol. We say things have a distance of "10 feet" away instead of a "closeness" of ?

For example: (pardon the notation)

1 X 2n {1,2,4,8,16..."infinite"} The "infinite" number is never reached but is the one the series reaches towards... infinite distance.

1 X 1/2n {1,1/2,1/4,1/8,...} Here "zero" is the number that is never reached but the one the series reaches towards... zero distance.

Negate the terms: the first series represents the progress towards "zero closeness" and the second represents the progress towards "infinite closeness."

So:
zero closeness is infinite distance, infinite closeness is zero distance

This sounds pretty strange, but I don't see the failure of the logic as of yet so I'll put it out for scrutiny.

Darth Dane

1 = 3/3

1/3 = 0,33333(of to infinity)
3*(1/3) = 3 * 0,33333(of to infinity)
3/3 = 0,99999(of to infinity)

1 = 0,99999(of to infinity)

How is this possible?

Imagine God is (1) and (3/3) is the Holy Trinity.

God = Holy Trinity

God's name is by God's words "I Am"

I Am = Holy Trinity

In language:

I Am the Holy Trinity

God Is the Holy Trinity

The Trinity consists of:

1) God(I Am)
2) Son(I Am)
3) Holy Ghost?

All three are infinite (0,33...)

God = HT

God Is 1 and doesn't move.

HT Is 0,99... and moves, as we can always add another number.

God Is the unmovable mover?


We as humans, are on the right side of the equation as this is where the trinity is.

Can we get infintely close to 1(God), but never quite there?


"This is the very perfection of a man, to find out his own imperfections." - St. Augustine




DD - Love Spliff

Hawkingfan

I think you're confusing "infinitely close" with "as close as possible" (without touching). I don't think the two are interchangeable. Infinitely close can mean that it is an infinitesimal (infinitely small) distance away from something. That does not mean it is as close as possible (or logically possible).

For instance, in your scientific and philosophical studies, have you come across Zeno's paradox? Zeno was a contemporary of Aristotle and came up with some theoretical paradoxes dealing with motion. But his most famous paradox deals with lines and infinity: If you got a line that is a certain length, with point A at one end and point B at the other end, the distance between the two points is the length of the line. To get from point A to point B, you first have to travel half the distance. You are halfway there. Then you travel half the remaining distance. And that distance is cut in half.
Each time you move closer, you cut the remaining distance in half. The problem is that you never get there, because no matter how many times you halve the distance, even when the distance gets INFINITESIMAL, it can STILL be cut in half.

Interestingly, the above description is similar to the THIRD LAW OF THERMODYNAMICS which says that you can make an object's temperature be absolute zero, but only in an infinite number of steps!! And it would take an infinite amount of time. It is not possible to reach absolute zero in a finite number of steps. But (here it comes) you can get infinitely close (meaning the distance is infinitesimal) to absolute zero. (Absolute zero in the sense of the 3LoT does not mean 0 degrees on any scale--it means the total absence of heat). Just think about Zeno. The distance is infinitely small, but you can always get smaller. That doesn't mean you can get as close as possible, because even in infinitely small distances, you can always get smaller.

Again, the 3LoT says that it is possible to get "infinitely close" to absolute zero, but you can always get just a little closer without getting there. (The science behind this is that it takes longer and longer to reach lower and lower temperatures. Whatever type of cooling system you use, it becomes less and less effective the lower the temperature goes down. That's just a hard fact of science).