On 26 Jan 2012, at 00:52, Craig Weinberg wrote:

## Advertising

This is what I am trying to say with Bruno about numbers starting from 1 instead of 0. From 1 we can subtract 1 and get 0,So we get 0 after all.Sure. Although 0 might be not be a number so much as neutralizing or clearing of the enumerating motive.

Not sure that zero has such a power.

but from 0, no logical concept of 1 need follow.No logical concept, you are right (although this is not so easy to proof). But you have the *arithmetical* (yes, *not* logical), notion of a number's successor, noted s(x). We assume that all numbers have successors. And we can even define 0 as the only one which is not a successor, by assuming Ax(~(0= s(x))) (for all number 0 is different from the successor of that number).Yeah, I can't see how 0 could be the successor of any number.

`Oh, but it makes sense though. If we were working with the integers,`

`then zero becomes a successor, it is the successor of -1, itself`

`successor of -2. They are quite genuine little citizens of Integer-Land!`

`From the point of view of computability they provide just an`

`equivalent theory of PA. PA already believes in the integers, in some`

`precise sense. We can use the rational numbers, too. But not the real`

`numbers, unless you add the trigonometrical functions, or second order`

`axioms.`

`I am not sanguine on the number. My heart pleads for the combinators`

`instead, but that would send the layman away.`

having the symbol 0, we can actually name all numbers: by 0, s(0), s(s(0)), s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), ...0 is just 0. 0 minus 0 is still 0.Yes. That's correct. And for all numbers x, you have also that x +0 =x. Worst: for all number x, x*0 = 0. That 0 is a famous number!Haha. I have always had sort of a dread about x*0. Sort of a remorseless destructive power there...

Better to avoid of being multiplied by zero, sure. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.