# Thread: The number line is a circle?

1. Any line has an equation of y=mx+b. Now, if we take the m(x) (read here as the slope of line x) and -m(x) where x>0, we find that a the x axis is equidistant from both these lines.

Therefore, -m(x)<m(h)<m(x) and |m(h)-m(x)|=|m(h)+m(x)| from this we can conclude that the slope of a horizontal line has a slope of 0.

Now if we take a similar observation, that these lines are also equidistant from the y axis, we find that -m(x)>m(v)>m(x) and |m(v)-m(x)|=|m(v)+m(x)|. However, this is, as far as we know, impossible.

Now I have just defined undefined. Now we must find a way to place it on a number line. We can make a few observations to help us:
1) it is neither positive nor negative
2) it is not equal to zero
3) it is greater than positive and less than negative

We'll name the number numerical infinity

We can draw one of two conclusions from this:
1) the number line is, in fact, a misnomer. It is a circle such that 0 and numerical infinity cut the circle into two arcs. One arc represents the postive numbers, one the negative numbers.
2) I am wrong.

2.

3. Originally Posted by Somanayr
Any line has an equation of y=mx+b.
nope

4. Is this thread worthy of continuation?

5. Originally Posted by Guitarist
Is this thread worthy of continuation?
nope

6. Originally Posted by DrRocket
Originally Posted by Somanayr
Any line has an equation of y=mx+b.
nope
This is slope intercept form.

Does anyone here actually say worthwhile stuff?

7. Somanayr is fifteen. Give the guy a break, or at the very least show him the inconsistencies, ambiguities, or misunderstandings in his thinking. Don't dump all over him. It is unseemly.

8. Originally Posted by Somanayr
We can draw one of two conclusions from this:
1) .....
2) I am wrong.
Yep

9. Originally Posted by Ophiolite
Somanayr is fifteen. Give the guy a break, or at the very least show him the inconsistencies, ambiguities, or misunderstandings in his thinking. Don't dump all over him. It is unseemly.
The reasoning presented is not up to fifteen-year-old standards. The logic is so bad that neither point-by-point critique nor and attempt to fix it are practicable.

It really is that bad.

10. Rocket You are too harsh. Our poster came up with the real projective line, perhaps by accident, perhaps not.

I freely grant that no coherent argument was presented for that extraction, in fact I agree the OP was pretty unhinged.

But I am inclined to agree with Ophiolite. So let the OPer tell us HOW the real projective line is found. This is a Math forum, so a proper argument is required, regardless of age

Hint to OPer: it has absolutely nothing to do with number line as it is usually understood. For sure, the term "number line" is NOT a misnomer, as you claimed

11. Originally Posted by Guitarist
Rocket You are too harsh. Our poster came up with the real projective line, perhaps by accident, perhaps not.

I freely grant that no coherent argument was presented for that extraction, in fact I agree the OP was pretty unhinged.

But I am inclined to agree with Ophiolite. So let the OPer tell us HOW the real projective line is found. This is a Math forum, so a proper argument is required, regardless of age

Hint to OPer: it has absolutely nothing to do with number line as it is usually understood. For sure, the term "number line" is NOT a misnomer, as you claimed
I am not nearly harsh enough.

The OP has nothing whatever to do with the one-point compactification of the line., or what you call the real projective line, except for the use of the word "circle.

That post is nothing but gibberish. It most certainly is not mathematics.
To pretend otherwise is to do a disservice to the OP himself and anyone reading this. GIGO

12. Somanayr, I cannot read your formulas without getting lost after the first few letters. Your math is completely confused.

However, there is a point to what you are saying about negative infinity meeting positive infinity. In some cases, in some situations, it is useful to think about them this way.

Think of the tangent function - as the angle approaches 90 degrees, the tangent runs away to +infinity, then "comes back" from -infinity.

Another, and very interesting situation, is in projective geometry. There, the infinite points at both "ends" of a line are indeed considered one point.

But please try to be more disciplined when you write formulas, so we all (including you!) can understand what you mean.

13. Originally Posted by DrRocket
I am not nearly harsh enough.

The OP has nothing whatever to do with the one-point compactification of the line., or what you call the real projective line, except for the use of the word "circle.

That post is nothing but gibberish. It most certainly is not mathematics.
To pretend otherwise is to do a disservice to the OP himself and anyone reading this. GIGO
Oh, for pity's sake, of course the OP was mathematical gibberish, of course he has never heard of the real projective line.

I was merely trying to draw the non-discussion away from the "Nope" and "this is wrong" sort of one-liners you seem so fond of to something that could be discussed, and something that our members might find interesting.

Leszek, bless him, was at least constructive in a similar sense.

14. Originally Posted by Guitarist
Originally Posted by DrRocket
I am not nearly harsh enough.

The OP has nothing whatever to do with the one-point compactification of the line., or what you call the real projective line, except for the use of the word "circle.

That post is nothing but gibberish. It most certainly is not mathematics.
To pretend otherwise is to do a disservice to the OP himself and anyone reading this. GIGO
Oh, for pity's sake, of course the OP was mathematical gibberish, of course he has never heard of the real projective line.

I was merely trying to draw the non-discussion away from the "Nope" and "this is wrong" sort of one-liners you seem so fond of to something that could be discussed, and something that our members might find interesting.

Leszek, bless him, was at least constructive in a similar sense.
Then start a new thread on projective geometry. The real projective line is of minimal interest in any case -- it is a circle. The real projective plane, on the other hand is topologically interesting. But there is no reasonable segue from the OP babble to this subject.

You can't make a silk purse out of a sow's ear, and in this case any self-respecting sow would be embarrassed to see her ear in such tawdry company anyway.

15. In theory you should be able to teach me quite a lot about mathematics. In practice it is unlikely you would be able to do so, since you would first have to learn a great deal about manners. There is no evidence that you would be suitable for instruction in this field. I imagine it's a curse of your superior intelligence.

16. This thread is getting bad-tempered. Were it not for the fact that I have been an active participant, I would lock it.

In other words, there seems to me no point in continuing a thread that merely creates bad feeling between members (Yeah, I made my contribution to that - sorry)

What think you all?

17. I'm not sure there is any bad temper as such, certainly not on my part. I simply object (and objected) to a verbally violent attack on a young and new forum member. If this had been on Jackson, or inow, or many others who are not only able to take care of themselves in the heat of debate, but have demonstrated that ability, I would have said nothing.

I was genuinely disappointed that you formed part of that attack, for it seemed quite out of character. I understand - as per comments by (In)Sanity that Dr Rocket is recognised for such behaviour. Perhaps he should be admonished, privately or publicly, then I wouldn't have to act like a prissy maiden aunt trying to climb to the moral high ground while wearing the stilletoes of hypocrisy.

18. Originally Posted by Ophiolite
I'm not sure there is any bad temper as such, certainly not on my part. I simply object (and objected) to a verbally violent attack on a young and new forum member. If this had been on Jackson, or inow, or many others who are not only able to take care of themselves in the heat of debate, but have demonstrated that ability, I would have said nothing.

I was genuinely disappointed that you formed part of that attack, for it seemed quite out of character. I understand - as per comments by (In)Sanity that Dr Rocket is recognised for such behaviour. Perhaps he should be admonished, privately or publicly, then I wouldn't have to act like a prissy maiden aunt trying to climb to the moral high ground while wearing the stilletoes of hypocrisy.
I have no regrets. If you will look closely you will see that my comments were directed at statements made in posts. It was your posts regarding the person of the OP that initiated any comments in that regard. I certainly did not check his birth certificate, and in the context of the material contained in the post age is irrelevant.

The very first sentence of the original post was a false statement, hence the simple reply "nope" to that assertion. That is a perfectly straightforward response to a false sentence. It should have prompted the OP to rethink his post.

The remainder of the OP was utter gibberish, lacking in either content or logic.

There is way too much encouragement of illogic and incorrect assertions in this forum and in society in general. I have no intention of jumping on that band wagon.

(In)Sanity can think what he likes, but his assertions ought to be taken as factual. He has had his own ax to grind as a result of a discussion on relativity in which he made his own major errors in logic and facts.

Mathematics is not a debate. It is based on some simple axioms an logic. Opiinion and debate have their place in some aspects of science, but not in mathematics.

The general attitude of laisez faire has resulted in a significant decline in mathematic education. I have recently been rather taken aback by statements made to me by research mathematicians at two major universities to the effect that incoming graduate students are no longer prepared for or capable of studying the ordinary theory of measure and integration. I can only acribe this to a lack of ability in basic logical reasoning, brought on by tolerance for illogic, since there are essentially no prerequisites for the study of that material (all you need are elementary concepts from naive set theory and the ability to reason).

Reasonable questions and inquiries from anyone, young, old or in between are deserving of reasonable explanatory and detailed answers. Gibberish and ridiculous assertions are not. In the face of gibberish and nonsense, the potential for transmitting incorrect information or reasoning to lurkers (also likely to be young) is of greater concern to me than the OP. Forums of this type usually have more lurkers than participants.

So, act the prissy maiden aunt if you want to. But I think you are trying to protectd the wrong people.

19. Originally Posted by DrRocket
In the face of gibberish and nonsense, the potential for transmitting incorrect information or reasoning to lurkers (also likely to be young) is of greater concern to me than the OP. Forums of this type usually have more lurkers than participants.

So, act the prissy maiden aunt if you want to. But I think you are trying to protectd the wrong people.
I am interested in the education of all persons, posters and lurkers. I wholly lack the knowledge to explain to the OP what was wrong with his ideas. You, apparently, do possess this knowledge (and, it seems, a desire to communicate it).

However, simply making the observation that the OP was talking rubbish really does not help anyone. I think you, or someone, dropped the Pauli quote - It's not even wrong. I understand that someone posts/statements are realistically beyond the ability of anyone to deconstruct in a fruitful way, but there remain more positive ways of critiquing them than an outright assault.

20. Originally Posted by Leszek Luchowski
Somanayr, I cannot read your formulas without getting lost after the first few letters. Your math is completely confused.

However, there is a point to what you are saying about negative infinity meeting positive infinity. In some cases, in some situations, it is useful to think about them this way.

Think of the tangent function - as the angle approaches 90 degrees, the tangent runs away to +infinity, then "comes back" from -infinity.

Another, and very interesting situation, is in projective geometry. There, the infinite points at both "ends" of a line are indeed considered one point.

But please try to be more disciplined when you write formulas, so we all (including you!) can understand what you mean.
I was pretty much just looking at a graph when I came up with this. The equations aren't too complicated, I just didn't put enough spacing .

Once I get back to a computer, I'll make an image. But basically, slopes gradually (or not so gradually) become greater, climbing towards a numerical (as opposed to conceptual) infinity as they climb towards vertical. From both the negative and positive directions. That gives us how infinity is neutral. And the only way to have two neutral numbers is to have a closed loop.

By the way, thanks to all who supported me. And Rocket, I'm fine with you critisizing me, but not without justification. I can say you live on the moon, but that does not make it true. Tax records, for example, would be evidence towards you living on the moon.

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