# Closest Number?

### #41

Posted 25 February 2004 - 09:52 PM

### #42

Posted 25 February 2004 - 11:28 PM

Let's say line A is the longer line, and line B is the shorter one. Let's say A has N(A) number of points, and B has N(B ) number of points. Let's assume that as Sip and Domino claim N(A)=N(B ).

A ________________________________________

B ______________________________

C __________

There is a third line, C which is the difference of A and B. Lenght(A)-length(B )=lenghtİ. Now, according to the same assumption, C has the same number of points as A, N(C )=N(A). Under normal assumptions lenght and number of points would be proportional - the more point you add to the line, the longer it is. So it follows that since length(B )+length(C )=length(A) then N(B )+N(C )=N(A). Since we assumed that N(B )=N(A) and N(C )=N(A), then we can substitute in the former equation and get N(A)+N(A)=N(A). Now, this is not true with finite numbers. Could this be true with infinite numbers? I would say that the answer is either no or undetermined. For all practical purposes the answer is yes. BUT...

Sasun jan those lines have exacly 2 end

**, this is 15 years of CAD talking, in our business and in drawings in general if its a line where it begins and ends paralel then can't have more then 2 points/endpoints.**

__points__### #43

Posted 25 February 2004 - 11:30 PM

**, this is 15 years of CAD talking, in our business and in drawings in general if its a line where it begins and ends paralel then can't have more then 2 points/endpoints.**

__points__Edo jan, what about the other points between the 2 endpoints

### #44

Posted 25 February 2004 - 11:33 PM

Hahahaha, Azat we do all the hard work, and you do the sweet talk? That's not fair. I think you should prove a theorem or two before you go to ladies I think ladies will agree with me on this

### #45

Posted 25 February 2004 - 11:35 PM

**Edited by Edward, 25 February 2004 - 11:36 PM.**

### #46

Posted 25 February 2004 - 11:35 PM

Nope, we like Azat just the way he is.

### #47

Posted 25 February 2004 - 11:41 PM

But but... have you ever considered the same Azat the way he is, plus he can prove a theorem

### #48

Posted 26 February 2004 - 12:18 AM

Let's say line A is the longer line, and line B is the shorter one. Let's say A has N(A) number of points, and B has N(B ) number of points. Let's assume that as Sip and Domino claim N(A)=N(B ).

A ________________________________________

B ______________________________

C __________

There is a third line, C which is the difference of A and B. Lenght(A)-length(B )=lenghtİ. Now, according to the same assumption, C has the same number of points as A, N(C )=N(A). Under normal assumptions lenght and number of points would be proportional - the more point you add to the line, the longer it is. So it follows that since length(B )+length(C )=length(A) then N(B )+N(C )=N(A). Since we assumed that N(B )=N(A) and N(C )=N(A), then we can substitute in the former equation and get N(A)+N(A)=N(A). Now, this is not true with finite numbers. Could this be true with infinite numbers? I would say that the answer is either no or undetermined. For all practical purposes the answer is yes. BUT...

sasun jan, there are only finite numbers, there is no such thing as "infinit" numbers.. We cant think of infiniti as a number, you cannot compute infitie plus infiniti... thats why it is abstrract, and that is the same case i am trying to mek.. lol..

and yes, line A B C all have the same amount of points

### #49

Posted 26 February 2004 - 01:17 AM

**the same number**of points.

are you sure?

i thought (2(inf))/(inf) = 2

### #50

Posted 26 February 2004 - 12:18 PM

and yes, line A B C all have the same amount of points

In mathematics, infinity is defined like this:

**number N is said to be infinitely large if no matter what number x we choose N>x always holds true.**

Now, you make up your mind to see if there is such a thing as infinite number or not

To claim that A, B and C have the same number of points implies that we know how many points each have. All we know is that each has an unknown number of points. We cannot compare unknown numbers. The only certainty is that no matter how large a number we think of, the number of points on each of the lines (A, B and C) is larger than that number.

However, 2 arguments.

One could argue that in order to get from B to A we do have to add more points.

One could also argue that in order to get from B to A we do not need to add points but only "stretch" B without adding more points.

### #51

Posted 26 February 2004 - 12:45 PM

i thought (2(inf))/(inf) = 2

Infinity divided by infinity?

### #52

Posted 26 February 2004 - 12:54 PM

Not necessarily. So here's how the proof goes ... in order to show that both have the same number of points, all we need to come up with is a 1 to 1 mapping from any point you pick on one line to a unique point on the other line.

To do this, we have:

/ a

/

Line 2: __/______

/ b

/

`p

I will pick a reference point p. For any point 'a' you pick on line 1, I will just draw the line connecting a to p. This will result a unique point b on line 2. Note that the order in which we pick points from the line (either from the shorter one or from the longer one) is arbitrary so this does in fact create a 1 to 1 mapping between any point on line x to any point on line y and vice versa.

The proof relies on some fundamental postulates but otherwise, it shows how both those lines have the same number of points!

### #53

Posted 26 February 2004 - 12:59 PM

You are right, I am surprised that Harut presented that, as it is one of the 7 undeterminated forms in mathematic, first you have to wave off the undetermination by the notion of limits...

But I do understand still Harut point, it could be seen as this.

lim (2x/x)

x -> inf

The answer to that will be 2.

But what Sip present is a different cases of infinity, and it is even debated among some mathematicians, I decided to not reveal the name of the mathematician as people will understand the whole point after a google search.

Edward and Sasun, the "Proof" is rather graphical, it can be translated by a demonstration form, but the beauty of it is very graphical.

### #54

Posted 26 February 2004 - 01:01 PM

But I do understand still Harut point, it could be seen as this.

lim (2x/x)

x -> inf

The answer to that will be 2.

But what Sip present is a different cases of infinity, and it is even debated among some mathematicians, I decided to not reveal the name of the mathematician as people will understand the whole point after a google search.

Edward and Sasun, the "Proof" is rather graphical, it can be translated by a demonstration form, but the beauty of it is very graphical.

Too late, Sip answered.

### #55

Posted 26 February 2004 - 01:02 PM

You still didn't say who came up with it. Unless you want to take credit for it!

Edit: Nevermind, just read your post.

### #56

Posted 26 February 2004 - 01:06 PM

Hmmmm.... No fair.... no fair... Saying it that way...

It was Cantor, one of my favoured. Not because he was mad and kind of schizophrenic.

### #57

Posted 26 February 2004 - 01:09 PM

But still there is something missing. How do you explain the difference C?

### #58

Posted 26 February 2004 - 01:11 PM

But still there is something missing. How do you explain the difference C?

In fact, there is something missing in his demonstration... but now that you have the name of the mathematician, just use google and voila.

### #59

Posted 26 February 2004 - 01:13 PM

What? that the point p is not arbitrary, and how to find that point?

### #60

Posted 26 February 2004 - 01:16 PM

**number N is said to be infinitely large if no matter what number x we choose N>x always holds true.**

Now, you make up your mind to see if there is such a thing as infinite number or not

Thats not the case here. That definition is most likely used to explain the notion of infiniti to high school kids at most.

I am saying if infiniti was considered the number N, then it is not infiniti, it is finite.. lol.. Because now N represents a "number" no matter how large it is, so thats why we call it infiniti, and it is neither a "variable" nor a number.. it is the "concept" of a value or N getting very very very large, how large? very very very very very large, then it keeps going.. LMAO..

ofcourse thats obviouse, but remember, do not refer to infiniti as a number, and you cannot try to proov anything with infiniti by incorporating it into various mathematical equations, formulas etc.....

you cannot call infiniti=N then say, 3N/N = N, no, but you can do what Domino did, take the limit, or differentiate...

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