Some quick questions up for discussion:
- Is infinity pluss one the same as infinity?
- Is infinity times two the same as infinity?
- What is infinity minus infinity?
- What is infinity divided by infinity?
- Is the reciprocal of infinity equal to zero?
- Can something infinite have a beginning?
These are dangerous questions. 🙂
Yes. And intriguing 😉
Because infinity describes an unassignably large quantity and is itself an expression but not a quantity per se, it doesn’t lend itself to calculations. Because it is not a quantity, neither is infinity describable as rational or irrational in the sense of without ratio. Yet, this becomes entangled in semantics, doesn’t it? The fact that Man abstracts such a concept is significant to me. But what does it mean, this infinity? To me, infinity is a notion which describes something like a never ending process, an idea, rather than a quantity like a whole number.
Wise answer methinks.
I’ll get back to you on that in half an infinity.
LOL
The notion of infinity for me points to opening doors of perception for additional dimensions of existence. Could “abstraction,” as the quality of dealing with ideas rather than events be such an additional dimension?
These questions surely have “by definition” answers.
Infinity is NaN, so the first 5 questions are meaningless (in the same way that a pizza + 1 is meaningless).
The last question, infinity by definition has no beginning. So the answer is no.
I would say somethiong like “Infinity is not quantifiable. It is the ground of quantity, the field within which quantity exists.” Trying to count infinities is like trying to count LRH’s “Statics”. We’re getting into the realm of the reification of abstracts..
Seems quite right to me.
My intuitive answers:
1. Yes.
2. Yes.
3. 0.
4. 1.
5. It’s undefined.
6. Yes, as long as it has no end. (At least that’s the definition of “infinito” in Spanish: anything that has no end. It doesn’t say anything about a beginning).
My thoughtful answer:
Infinity is an idea, not a number. Thus, it’s not mathematically operative (although it has some mathematical properties).
Thanks for another interesting post. These questions suggest that there’s something wrong with the concept of infinity. I’ve never seen an infinity, maybe it’s just a concept that mathematicians invented to answer other difficult questions like “where do parallel lines intersect?”
Alternatively, we could try Boolean algebra and say that infinity is equivalent to 1, the whole universe of discourse. Then:
1. 1 + 1 = 1
2. 1 multiplied by 2 = 1 (same thing as the previous question)
3. 1 – 1 = 0
4. 1/1 = 1
5. 1/1 = 1 again
6. Not a mathematical question. ‘Beginning’ is another of those concepts that we’ve inherited and taken for granted. What if things don’t actually begin or end, they just are or are not?
Thanks for an interesting reply.
Is infinity plus one the same as infinity?
Yes – Infinity plus anything is infinity
Is infinity times two the same as infinity?
Yes – Infinity times two is infinity
What is infinity minus infinity?
Is infinity of no infinity
What is infinity divided by infinity?
Infinity
Is the reciprocal of infinity equal to zero?
No
Can something infinite have a beginning?
Yes – Eg: Start with any number and divide it by half.
Now dividing by half again and again and never stop.
You have a begging but no end.
Infinity.
Things like zero and infinity need to be defined in detail for a particular question to get an accurate as possible answer for that particular question.
But what is the point of these questions?
Its like asking
“How long is a piece of string?”
Relevant: http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Next to the tragic story of Alan Touring, comes the horrific tale of the wonderful Dr. Georg Cantor.
Cantor is the father of the maths of infinity and he was driven insane and ruined financially by a colleague named Leopold Kroneker who was out to literally destroy his career and maths.
And for the most part, he did destroy the man, but his ideas were bullet proof.
We are lucky to have the brilliance of this man still with us.
MY TEST ANSWERS:
Is infinity pluss one the same as infinity? (Yes.)
Is infinity times two the same as infinity? (Yes.)
What is infinity minus infinity? (Depends on the cardinality of the infinity as some infinities are larger than others. That said, Aleph Zero minus Aleph Zero is zero.)
What is infinity divided by infinity? (Again, I think it depends on the cardinality.)
Is the reciprocal of infinity equal to zero? (Donno.)
Can something infinite have a beginning? (Infinite series do have definite beginnings, but that
But the real question NOT asked is “Does Infinity ACTUALLY equal -1/12th?
Yes. Yes it does IMHO.
Oops.
“Can something infinite have a beginning? (Infinite series do have definite beginnings, but that is dependent upon a being starting the series in a place where time is infinite and it time is an illusion does it exist? FUCK if I know.)”
I am a Pythagorean by nature and a mathematical realist like Godel. For me infinity and nothing are not notions but THE notions.
BTW: Ran across the best book ever. I did find a mistake on the page discussing the number three though. This book is fucking awesome. I’m about to order their book on sacred geometry out of hopes it isn’t all woo-woo.
http://www.amazon.com/Quadrivium-Classical-Liberal-Geometry-Cosmology/dp/0802778135/ref=sr_1_1?ie=UTF8&qid=1420432415&sr=8-1&keywords=the+quadrivium
A lot of people don’t get WHAT this is. It is the re-creation of the core curriculum of Pythagoras and Plato that were lost – updated with modern information regarding the cosmos. I’m sure there are things still missing that we will never know. But still, it is a GREAT piece of work.
In mathematics ‘infinity’ is a number with no end. Consequently, some assume the concept of infinity to be something vast, great, wow. So, if you say you are ‘infinity’ some assume you have too big an idea of yourself.
In SCN infinity meant that which includes all that is and all that can be. It is not something measurable, because it refers to potential existence. And it includes everything. Subsequently, all is infinity.
Something that has a beginning and no end, is called eternal –endless time. It has nothing to do with infinity as ‘endless potential for existence’ (or no existence).
Mathematics don’t measure things that are not, but can be. As those things don’t exist. Thus we also have or used to have in ancient Athens philosophy –some good, some lame, you judge that.
We create the idea of an infinity. As soon as we created it as an idea, it had a beginning.
Hehe
Yes, to contain something into an idea is a limitation in the first place. Thus, not infinite. And that doesn’t stand for the subject of infinity, alone. You could say something like ‘John (random name) is stupid’. But how true would that be? John could be stupid in one moment and clever in another or he could be whatever… To be eager for conclusions, is to limit things from further knowing about them, not to mention from freely creating them. If ‘John is hostile’ is true, then I couldn’t possibly get along with him, right? Still, for me, no standardness is true. Things can be different than they used to be. They can also not be anymore. And new things can come to exist that hadn’t existed before. John can be anything.
1.undefined
2.undefined
3.undefined
4.undefined
5.no, it’s undefined
6.Good Question equivalent to the principle of Well-Ordering! See the controversy re Zorn’s Lemma/The Axiom of Choice.
Infinity is not an algebraic number hence the common algebraic properties associated with algebraic numbers do not apply. There are in fact a variety of transfinite numbers (i.e. “infinities”). The “algebra” of transfinites has it’s own rules predicated on set theoretic considerations which avoids apparent inconsistencies which arise due to commonly held inherent misconceptions. See Georg Cantor’s Theory of Transfinite Numbers.
Yup.
As one example, the series “1,2,3,4…” is clearly not equal to the series “1,1,2,3,4…”.
Could this express a non-well ordered set: ( . . . ) ?
I’ve attempted to write a set without beginning or least member and without an endin. I’ve also failed or simply not defined a beginning nor an ending of what. At least that’s what I tried to do. It is a little bit nonsense but, uh well, there it is.
No beginning, no end : “… – 3,-2,-1,0,1,2,3…”
Ah, I see that.
That leads to all kinds of weirdness, as indeed, the old saw about going “half the distance, then half the distance etc” but never arriving might be one….
However, what, in real terms, is a negative number? If we’re talking about things that do not exist, why bother? Why not just read or write sci-fi? Or live life?
Perhaps -1, -2 etc could be construed as the vanishment of some existing things; in that case, in an infinite universe, one could go on as-ising things forever and never actually as-is the whole universe. There would always be more, to infinity….
And why restrict yourself to + and – values? Those constitute a Line. Why not have some values at right angles to those? Extend it to 2 dimensions, and then again, to 3 dimensions. Wouldn’t that be a hoot!
Negative value: I owe you $5, I have -$5.
Symbolism!
There’s life and assumptions underlying these questions
Did we begin the idea of infinity or did it exist before we did?
What are we and are we capable of measuring or reproducing our results?
We need an infinity stick to measure it
can two infinities exist in the same space?
Maybe if you add one to infinity it becomes something else, who has a 1?
If you divide infinity maybe you get infinity x 2 is it like a worm which can reproduce?
Infinity to me seems to be a continuous inward and outward flow, maybe it’s only two dimensional so we cannot really see it or maybe it’s just a 4th dimension
To beat a dead horse what did Lafayette say about infinity?
It’s been over three hours since I entered these equations concerning infinity into an advanced mathematics program.
The computer is taking forever.
Patience my friend. Patience.
Oh my! Wot a pity, we think we NEED to understand, before we reach enlightenment? It’s just not done, to simply KNOW, or is it??? 🙂