Line is a Circle

Okay a line is a circle of infinite diameter

Well, the only reason that you would have made such an assumption is because such a circle would have no apparent curvature. You're clearly contradicting yourself.

Anyhow this is just stupid, Cormac, I hope you get lambasted by stiff arses with no concept of intuitive mathematics but with an obsessive and needless necessity for "rigorous" mathematical convention.

Just being bitter at this hour of the morning. Oh and the "QED" in your signature isn't very appropriate.

You state that a circle of infinite radius is a line. Then you go on to deny the reason that this assumption is true.

And tell me cormac, what is the difference between infinitely small.. and zero?

You should really have written "straight line" in your original post methinks.

Isn't it completely obvious that a circle of infinite radius would still be curved so would therefore not be straight hence nullifying the hypothesis that curvy=straight?

Or that could be what bonkey is saying . God I used to be great at maths until I moved to a country that allows underage drinking!

If you want to "ruin" maths look for the omega number (apparently). Like the comma of life, the omega number is something that doesn't add up, it is something that cannot be calculated but exists. Ah heck I don't know really, I just like reading the New Scientist.

Well, this all began with this post.

Originally posted by Sev
Hehe, me and Davey (PHB) have this running joke now about the value of 0/0

Some say its 0 as its 0 over a number. Some say its infinity because its a number over 0, and some say its 1. Its essentially infinity/infinity, which is the same as 6/6 which is the same as 5/5 which equals 1, so as far as im concerned the answer is 1.

But the question is so utterly stupid and trivial, I like to think of it as a question of faith. What do you believe?

I knew making that post, that there would be some who would take exceptions to what I had said, and not understood the underlying gest of the post. Which is why, I tried (for a moment) to dismiss the explicit technicalities of the mathematics and relate to it on a sheerly practical level to provoke a sense of humour I guess.

But the biggest mistake I ever made, was thinking that people would automatically understand me. For example, naturally I don't mean "intuition" in the most literal sense. I dont believe 6+4 is 10, because I 'feel' it is, but rather because I know it is. Because I instinctively grasp mathematics in a way that many others can't.

The fact that there would need to be a proof for why 1+1=2, simply annoys me. The concept is so unbelieveably strikingly obvious, and the proof is nothing but an attempt to try to put into mathematical logic what any normal brain would automatically assess without second thought. Seriously, it makes me want to lash out and hurt people. I had hoped the majority would automatically agree, but it appears now, to my surprise, that there are many, (yourself included I think), who feel that such a proof (and such trivial mathematics that relates) has importance and is worth the effort to even explain in its own merit.

I make my arguments (if you can say I ever had any), in the same sense that underlines the core of the subject of my running debate. That such trivialities are so benal that there is no need to even explain thoroughly my reasoning, but that most would take for granted the fundamental obviousness of what I'm saying, and just accept and understand based on experience. Clearly I was wrong. People do NOT think like I do, and some just take things quite literally.

You seem quite fond of highlighting what I find to be strikingly obvious, to present your case, in such away that it appears quite condescending, as if I hadn't already realised. But I guess thats a personal trait, and reflects your mindset with which you approach a logical argument, wether it be verbal or mathematical. Although I accept that nothing you have ever said has actually been flawed or incorrect, but in my opinion , it has neither affected, discounted or disproven my beliefs too. We just have rudimentary differences in our thought process. I aplogise for the cheap stab I made earlier in this thread.

With that in mind, I don't believe there is anything I have ever said on these boards that has been logically 'flawed', if only for the reason that it doesnt comply with standardised mathematical convention and procedure. Ive always held the view that some people can be taught maths, whereas some don't need to be.

I would appreciate if you would not try to break down the points of what I have said now to refute and negate in some kind of strictly logical, exclusive, procedural way. That will just show you have completely missed or misunderstood the fundamental message of this argument. If people cannot still come to terms with what I'm saying, then I have failed, I give up.

I did not say that maths was subjective.

Originally posted by ecksor
I suppose I sound condescending again, but bear in mind that you sound equally condescending when you tell us what to think about things you don't appear to understand.

Now that.. that is subjective.

Originally posted by ecksor

But, again, I come back to my usual questions "what set is this" and "how do you define +". Supposing that the set is all the integers from 0 to 7 inclusive and that + is the operation of modulo arithmetic, then 10 doesn't even exist in that set, and most certainly isn't the correct answer. You might feel that this is irrelevant, but perhaps the triviality that such a proof is investigating can illuminate something about the nature of sets where 6+4 = 10 under either operation or something about a more general case.

(on that note, 1+1=0, haven't you heard of ecksor? )

Regardless, you just proved (unintentionally it seems) that maths can be subjective.

(I hope you considered that the word can have a number of definitions and interpretations)

I hope you realise, that by 'subjective', in the quote which you have paraphrased, I was referring to a specific use of mathematical "language", language which in general can have different interpretations, uses and meanings depending on the conditions in which it is used and the goal of its application. You appear to clearly agree, as you have shown in your previous post, which would mean that you are either now contradicting yourself, or could not understand me the first time.

Obviously I know you know exactly what you're talking about, there was never any doubt, and this argument has been reduced to a game of semantics (was it ever not?). I was just turning your post around to show that your original point, that you feel I don't know what I was talking about, was entirely uncalled for, and if you'll allow me to use that ridiculously vague and equivocal word, which you seem to center the core of that argument around... subjective.

Originally posted by ecksor
Hm, a few minutes ago this read something like "Didn't you just prove", and then you deleted it so you could assert "you just proved" when I did no such thing. Unintentional was it? How clever of you.

I have an obsessive compulsive disorder with posting and in general too. I tend to delete and repost about 3 times before I'm totally happy with what I have said. Either way both get the message across. The latter seemed more definite.

You might want to check up the meaning of the word "rhetorical question" when you look up "subjective".

My previous post, that I take it you havn't read yet, should clear up your other queries.

Originally posted by Sev
I hope you realise that there are many who would agree with me, they just dont seem to make their voices heard on this forum.

So what?

If I said that the earth was flat, there would be many who would agree with me. It still doesnt make my assertion any more (or less) valid.

And another newsflash for you...it doesnt actually matter what you believe mathematical language was created for, no more than it matters if you believe that "1+1" must intuitively be 2. Belief and correctness are entirely seperate issues.


If you dont want to believe that mathematical language exists to remove ambiguity, then ask yourself how 1+1 can always equal 2, unless 1, 2, + and = are all unchanging and consistent in their meaning and behaviour...which means that they are entirely unsubjective, unchanging and unabmbiguous. The entire language behaves in the same manner, for ambiguity would destroy the entire foundation that mathematics is based on.

Whether or not you like this, believe this, or accept this doesnt change the facts. It may not even be intuitive to you....but mathematicians frankly wont care. They know and understand why it is not subjective, not ambiguous, and why it cannot be. Just because you desire to avoid admitting your wrong or genuinely believe otherwise still doesnt change anything.

You can argue your semantics all you like. You're still wrong.

jc

Well bonkey, Its amazing how quick people jump to think that you are trying to refute an entirely unrelated argument with a simple, innocent point. I never disagreed with you, if anything I praised you. In fact, there is not much that anybody has said that I disagree with.

As for ambiguity, I would have thought mathematics was riddled with ambiguity, lets take a quick look at google.

Could you tell me, exactly, how many roots has any run of the mill 2nd order diophantine equation? You may want to do a little reading on Kurt Gödel's Incompleteness Theorem too.

In 1931, the Czech-born mathematician Kurt Gödel demonstrated that within any given branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules an axioms, but by doing so you'll only create a larger system with its own unprovable statements. The implication is that all logical system of any complexity are, by definition, incomplete; each of them contains, at any given time, more true statements than it can possibly prove according to its own defining set of rules.

Apart from that, what exactly is it that im wrong about?

Originally posted by Sev
As for ambiguity, I would have thought mathematics was riddled with ambiguity, lets take a quick look at google.

I was referring to the language of mathematics being unambiguous, rather than its ability to produce ambiguous statements. You will also find that this is the point Ecksor has been making from the start, which you have been disagreeing with.

You may want to do a little reading on Kurt Gödel's Incompleteness Theorem too.

Its ok thanks. I studied it fairly extensively about a decade ago.

I understand what the theory says, and what its implications are. I know why it isnt terribly relevant to the discussion at hand -for the reason stated above.

And I don't need to google for it either thanks. If I had to do that, I wouldnt know enough to be able to discss the point in the first place - just appear like I did until someone who actually knew what they were talking about decided to take me up on some point.

Apart from that, what exactly is it that im wrong about?

Go back and read my post. You'll find that I already specified what you're wrong about. I have no inclination of repeating myself.

jc