Consider the title of this post while reading this. I will admit that, when first approached by this idea, it seemed a little much. After taking the time to ponder it, It eventually hit me as easy to stomach. It required some mental yoga, but the idea that no 2 things are alike, means, nothing is alike. Having had logic classes, I know that one can argue the case, lets not get mired here.
When no 2 things are alike then no 2 things are alike. This includes 2 nothings.
So, What can you do when 2 things (i.e. nothing) are alike, you can add. So as some of our more illustrious posters admitted, that yes, his math is circular. Well that's fine. y=mx+b can when solved for zero certainly looks like 0=0 when b=0, regardless of m. A mathematical proof need only prove itself.
You need to define "nothing", "alike" and then show mathematically that 2 nothings are alike. Then you have to define the operation of addition for alike nothings.
Mathematical
proofs that use circular logic are wrong. Your example is not a proof - it is a calculation.
Mr. Check, the fundamental concept of zero is a place holder for nothing. When I said that bookkeepers in India several thousand years ago gave us this concept, it came from an accounting standpoint. The ZERO sum is a useful tool when calculating balances, IE when the miller has received nothing from his customer, the baker. Keep in mind, before this point a lot of great work had been done without in geometry, astronomy etc. I am getting off track here, but I hope we can see eye to eye here.
...snip Zero stuff...
That is right - if you have a definition for addition.
Terence Witt never defines addition in null geometry. He assumes that he can use arithmetic addition of numbers on the symbols that he in his definition of a line. But the zeros in his line are not the number zero. They are points.
By treating the zeros in his definition as numbers rather than pointshe is invalidating his definition of a "line".
Here is a another definiton for his "line":
A line is "...+X+X+X+X..." where the Xs represent geometric points and "a point has no mass, charge, or any other property, except for its position relative to other points".
Now add the X's together using ordinary arithemetic.
What about this definnition of a line:
A line is ".../0/0/0/0/..." where the zeros represent geometric points and "a point has no mass, charge, or any other property, except for its position relative to other points".
Now divide the zeros using ordinary arithemetic.