We can apply the concept of infinity PARTIALLY, always PARTIALLY, to imaginary numbers.
But infinite numbers are never expressed. They cannot be expressed. In any fashion.
When infinity is used in mathematics it is always some conceptual trick using other concepts like limits. And the math is always an approximation. An approximation that is good enough for the real world.
How many places do we have to round things out in the real world to send a rover to Mars? Infinite?
If people make the claim that something is real it is not unreasonable to ask for the evidence.
But really all I want is a demonstration that this non-quantity "infinity" could even possibly be real. What would it mean to move an infinitely small distance? What distance is that?
Of course in the backwards sense, the terminal point is the beginning, which if the sequence really were infinite, there would be
no beginning.
Yes it reduces to absurdity quickly.
What does it mean that something progresses yet somehow never starts it's progression?
That is a miraculous absurd state. Not a real world state.
Certainly not an answer any adult would take seriously.
Thank you for your reply,
untermnesche. Some of it I can agree with, some not, and some is purely of interest.
I'll expand on that now, please read, understand and reply as you see fit. I'll put quotations from your posting in braces
thus : { } . . .
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{We can apply the concept of infinity PARTIALLY, always PARTIALLY, to imaginary numbers.}
My comment: You're obviously not a mathematician,
untermnesche, because in mathematics, real numbers are defined,
and are defined to be in contrast to imaginary numbers.
Numbers like 1, 2, 3, 4.5 etc are called real numbers, in part because they can be used to describe the quantity or magnitude
of things in the real world. For example we can have, one apple, two oranges, three blind mice and be four and a half years old.
Imaginary numbers are an invention to extend mathematics, in a coherent fashion. The value of the square root of minus one,
(
) is an imaginary number.
The value of
is not
"1" , because the rules of arithmetic say that 1 x 1 = 1 , so
is not
"1"
The value of
is not
"-1" , because the rules of arithmetic say that -1 x -1 = +1 so
is not
"-1"
There is no value which can be multiplied by itself to get "-1", ("negative times negative" = "positive").
So there is no real number that can be derived as "the square root of -1". The value "the square root of -1"
is given the label
i . ("
i" stands for imaginary number). However, we can imagine that
i is a number, and
as a consequence
x
=
1
I'll accept that what you mean when you say {imaginary numbers},
untermensche, is that pure numbers are constructs, not
in the real world as such. However, the mathematical concept of real numbers can be descriptive of quantity or magnitude of things
in the real world, which I suggest
you'd qualify as real things. As an aside, I'd point out that time is not a real thing in the sense
that you are using the word "real". You can't pull out and look at the
number "5"]/u] for example, nor can you pull out and look at a
second, a minutes or an hour, etc. So time looks a lot like the numbers you are calling "imaginary". By that logic then,
if there is an infinity o positive whole numbers, (no terminal), why not an infinity of time?
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{But infinite numbers are never expressed. They cannot be expressed. In any fashion}.
I'm not sure from that quote, untermensche, what you mean by {expressed} in your statement. The meaning of, "expressed" in your statement is unclear.
Here it is expressed:
My guess is that you are saying that it is impossible to identify an infinity of real things in the real world.
You call infinity a number, or collectively {infinite numbers}, but that expression seems to fly-in-the-face of your contentions about infinity - just saying.
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{How many places do we have to round things out in the real world to send a rover to Mars? Infinite?}
The answer is no, but that is entirely irrelevant to the question of whether it is possible or not for infinities to exist. In this question, You've introduced
the idea of numbers as being real. To get to Mars, you need to apply numbers. But what is the value of 1/8 ? Answer, it's 0.125
1/8 is has a decimal value with three places. But pi is a number whose value is the ratio of the of a circle's circumference, to
its diameter. The value of that ration, if calculated, has no terminal value. As such, we have to round it off, for it to be useful in every
day applications. The fact that we round pi of does not mean that it has a terminal decimal place, and so the value of pi could
be calculated ad infinitum, if we had the time. So rounding off has no bearing on negating the question we're discussing, untermnsche.
In fact, the need to round off is in part due to the non-endingness of the real value of pi, the ratio of the of a cricle's circumference, to
its diameter).
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{If people make the claim that something is real it is not unreasonable to ask for the evidence}.
Well, untermnesche, I have not made such a claim. I'm say: "I don't know, (yet)".
Likewise, if people make the claim that something is NOT real it is not unreasonable to ask for the proof.
To say it's absurd is no proof, and all arguments so far have not been convincing in saying infinities in the real world, applied to real objects,
or time duration, or events, are impossible. A mere declaration of absurdity doesn't 'cut-the-mustard' for me.
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{What does it mean that something progresses yet somehow never starts it's progression?
That is a miraculous absurd state. Not a real world state.
Certainly not an answer any adult would take seriously}.
Let me take the last bit first. Scientists are adults, and some are better informed, and understand the nature of physical reality much better
than me, (and I'd suggest better than you, untermnesche). Yet some scientists whose business it is to think about, and investigate
these matters suggest just what we are discussing, namely that time can be infinite into the past. I can show you the evidence of that, or
do you do them the insult of calling them not adult ???
One way of looking at it is to say that every event must have a cause, so every event must be preceded by that cause. If every event must
have a cause, then there smut always be something before, no matter how far back one might imagine going. The religious will try to terminate
the infinite regress by positing a first cause, ("God"), but that's a miraculous declaration, and also a matter of special pleading, which is a logical
fallacy - they''d just like it to be true that "God" was, (is), responsible). If s you say something {starts its progression}, what do you propose as
the first cause, untermensche? Of course without a first cause, (infinite past), there is no first cause problem.
I like it where you link the {miraculous}, to the {absurd} ~ really 
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I hope you'll read all of this thoroughly, and respond if you find anything erroneous.
Al the best, Pops.
P.S. I have loads more to say, but I've spent enough time on this post today. I'l check back tomorrow, (South Australian time).
- - - Updated - - -
All of your objections have been addressed in this thread....
That is one big fucking lie.
Nobody has told me how a real completed infinity is a rational idea.
Nobody has told me how such a thing could possibly be possible?
Do infinities complete?
I just spied this post of yours, untermnesche, and I intend to get around to it, with your co-operation.
Cheers, Pops.
