Odd and even infinities: Philosophy Forums

Page: 1 2 3 4 5 6 7

Odd and even infinities

former
banned

Usergroup: Members
Joined: Aug 06, 2009

Total Topics: 13
Total Posts: 91

Posted 08/14/09 - 02:06 AM:	#61
You are always hostile toward views you don't understand? Or just in this case? "Demand that we change anything about how we use mathematics." Again I don't see what is the sense of what you are saying or in saying it. I don't think you understand the purpose of a definition in mathematics well which is different than that of other sciences and philosophy. As I already said, I'm done playing the all-knowing caterpillar from Alice in Wonderland for I'll be busy this week. Do your thinking alone. Edited by hyena in petticoat on 08/19/09 - 09:27 PM. Reason: Illiteracy.

Kwalish Kid
Tenured Poster

Usergroup: Members
Joined: Sep 26, 2004

Total Topics: 33
Total Posts: 3844

Posted 08/14/09 - 03:37 AM:	#62
former wrote: you are always hostile toward views you don't understand? or just in this case? I am hostile to people who make little attempt to explain themselves, use poor English grammar and make no attempts to use capitalization, punctuation, or paragraph structure. Such a format engenders a hostile response from many, I imagine. "demand that we change anything about how we use mathematics" again i don't see what is the sense of what you are saying. or in saying it. i don't think you understand the purpose of a definition in mathematics well which is diffrent than that of other sciences and philo. No, I understand it fine. What I don't understand is the basis for your claims that the definition that I gave for "odd" is wrong, given that there is absolutely no consequence to defining it in any way and that I was attempting to give a definition that was matching the use of someone other than you. Additionally, that person essentially agreed with my definition. In mathematics we can begin with a number of definitions, but if we want to change definitions, it's usually because there is a point to the change. So far, you have not shown a good reason to abandon beno's definition.
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P Can you pass Religion 101?

former
banned

Usergroup: Members
Joined: Aug 06, 2009

Total Topics: 13
Total Posts: 91

Posted 08/14/09 - 04:25 AM:	#63
I didn't say that your definition of "odd" is wrong. I say that it is different than my definition. I define odd as not-even. And you define it as "could-be-breaked-into-3" It really doesn't matter as long as you can follow the different meaning. You seem to want the "true" definition. while I want a "better" definition. I admit that your definition is in better accordance with beno's first intuition. Let's accept that odd is "could-be-breaked-into-2-with-leftover" and even is "could-be-breaked-into-two". Then I can prove that if a set is odd he is even and if a set is even he is odd. Being odd and even is the same thing. But that's not so bad. I have also proved that every infinite set is even. This proof uses the theorem that \|x\|+\|y\|=max(\|x\|,\|y\|) which you prove in set-theory class in about one paper. So your statement that "there is nothing difficult in this thread" is very relative. Indeed there is nothing difficult in mathematics after you have the right proof. But you seem to say... "Ahh.. This doesn't seem difficult although I can't prove it" which I can't appreciate. Anyway, I think I have concluded all that can be said about odd and even sets. All sets are even and odd at the same time by your definition and all sets are even and no set is odd, by my definition. Which is one and the same thing Edited by hyena in petticoat on 08/19/09 - 09:24 PM. Reason: Illiteracy.

AKG
Tenured Poster

Usergroup: Members
Joined: Jan 15, 2004
Location: Berkeley, CA

Total Topics: 87
Total Posts: 3329

Posted 08/15/09 - 11:36 PM:	#64
The closed real interval [0,1] can be put into bijection with [0,1). Define f : [0,1] -> [0,1) by f(x) = x/2 if x = 2^(-n) for some n = 0, 1, 2, ... f(x) = x otherwise Indeed any infinite set can be put into bijection with itself-minus-one-element. This is easy to prove with the axiom of choice, off the top of my head I'm not sure if it can be proved without it. At any rate, without AC it's easy to prove that if there is a bijection f : X -> Y, then there is a bijection g : X -> X with g(x) =/= x for all x and g(g(x)) = x for all x if and only if there is a bijection h : Y -> Y with h(y) =/= y for all y and h(h(y)) = y for all y Since the bijection [0,1] -> [0,1) was constructed without AC, it holds that [0,1] is "even" iff [0,1) is "even" without AC. Of course with AC it's routine to show that every infinite set has a bijection with itself which fixes no points but is the identity when composed with itself, i.e. every infinite set is "even."
"The only reason we die... is because we accept it as an inevitability." -- Stewie "To enslave nuance to dogma is folly." -- Lord Hillyer

Uncertainty Principl
Aspirant

Usergroup: Members
Joined: Aug 12, 2009

Total Topics: 0
Total Posts: 26

Posted 08/16/09 - 04:03 AM: Subject: Odd and even infinities	#65
I want to make one more observation about some of the conclusions that have been drawn so far in this ongoing discussion. Kwalish Kid stated that eliminating every other number would inevitably lead to the conclusion that infinity is both positive and negative. I was initially willing to accept this interpretation; however, this is using two different values for infinity. Adding even one value to infinity changes the current infinity you are working with. It cannot be determined to be even and then add one more value to it and then say that it is odd. The current task is to determine whether infinity is divisible by an even or odd number--a task which I do not see any realistic way to accomplish as I have already explained earlier in this discussion.

ssu
Graduate

Usergroup: Members
Joined: Jun 02, 2007

Total Topics: 5
Total Posts: 217

Posted 08/25/09 - 12:56 PM:	#66
Uncertainty Principle wrote: The current task is to determine whether infinity is divisible by an even or odd number--a task which I do not see any realistic way to accomplish as I have already explained earlier in this discussion. In my view the problem is that people think that what applies finite numbers, applies to the infinite. Thinking if infinity is a even or an odd number sounds very peculiar.

Page: 1 2 3 4 5 6 7

Sorry, you don't have permission to post. Log in, or register if you haven't yet.