20220201, 19:23  #1 
Aug 2020
Guarujá  Brasil
59 Posts 
The quantity of integers distributed along the number line is an odd quantity
In the XYplane we have the Xaxis and the Yaxis, each with a number line containing all integers.
So, if we make the bijection between the positive numbers on the X and Y axis, then we can say that the number of positive elements on both axes is an even number. The same is true for negative integers. So, if we now consider that zero has no corresponding pair, then we can state that the quantity of integers distributed along the X and Y axes in 2D of the XY plane is an odd quantity. Similarly, this reasoning can be done for the 1D number line and also for 3D space. All of them have an odd number of integers distributed along their axes. Is this reasoning correct? Does anyone see anything that has not been considered? Thank you, 
20220201, 20:04  #2  
Feb 2017
Nowhere
3×11×181 Posts 
Quote:
Further, "positive numbers" and "positive elements" on a coordinate axis means positive real numbers, not just integers. Quote:


20220201, 20:07  #3  
Sep 2002
Database er0rr
2×3×23×31 Posts 
Quote:
Last fiddled with by paulunderwood on 20220201 at 20:18 

20220201, 20:59  #4 
"Curtis"
Feb 2005
Riverside, CA
5,471 Posts 
Why can you say it is even? What does "the bijection" have to do with it? Be specific here you're reaching meaningless conclusions because you're waving your hands without considering the meaning of the words you're using.

20220201, 22:41  #5  
Aug 2020
Guarujá  Brasil
73_{8} Posts 
Quote:
Now, can the cardinality of all positive and negative integers (A+B) without the number zero, be considered as an even cardinality? 

20220201, 22:45  #6 
"Rashid Naimi"
Oct 2015
Remote to Here/There
8EF_{16} Posts 
Even numbers can be bisected to even numbers. Any way you look at it it does not follow that the number of positive integers is odd (or even for that matter).
Last fiddled with by a1call on 20220201 at 22:46 
20220201, 22:48  #7  
Sep 2002
Database er0rr
4278_{10} Posts 
Quote:
Also \(\aleph_0 + \aleph_0\ = \aleph_0\). See: https://en.wikipedia.org/wiki/Cardinality 

20220201, 22:56  #8  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,287 Posts 
Quote:
There is a onetoone relationship between all positive integers to all negative integers and 0 is the tiebreaker making an odd total. While that argument works for finite sets, it does not follow that it will hold true for infinite sets. There is a oneto one relationship between all countable infinite sets. So there is a onetoone relationship between any infinite subset of integers (say all multiples of 19) and complete set of integers. Normal rationales break down when dealing with infinites. 

20220201, 23:42  #9 
Feb 2017
Nowhere
3·11·181 Posts 
No. I've already explained. So have others. You're obviously not paying any attention.

20220202, 00:22  #10 
"Curtis"
Feb 2005
Riverside, CA
5,471 Posts 

20220202, 03:43  #11 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5·1,319 Posts 
Isn't there an unspoken assumption that the axes must always cross through (0,0)?
I could just as (in)correctly state that all axes cross at (1,1), thus zero has two instances on each of the X and Y axes. And that since one is common to both axes then there only a single one, so there are fewer odd numbers than even numbers. Indeed there are an infinite number of places we can put the crossing point of each axis. Crossing at (0,0) is an arbitrary choice. BTW I had to write two zeros (0,0) when defining the point. So does that mean there is more than one zero anyway? Last fiddled with by retina on 20220202 at 03:47 
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