Defining Unity

100101011101110100100100111010100101 Is there a simpler code?

...1, -1, 1, -1, 1, -1, 1...

Same difference! This is still just two symbols.

One could also use spaces, but the spaces are the presence of an absence. Zeroes or negative ones are just convenient ways to represent what a space represents.
1 111 1 1 1 111 1 1 111 1 1 1 1 1 1

I am sorry, the spaces are just for the purpose of not reading eleven...the point was about not changing to mutch from One to anything else...something like, one, and not one has the shadow of one....

So, for the purpose in here, not one, (-1), represents zero...(I am pointing to a false absence...)

Frege mentions the difficulty of defining unity in his book on arithmetic. I agree. I think it's an intuition, something hard-wired. But that's just my opinion. I invite you to define unity, or oneness, etc. You can use synonyms, but that's not ideal, for obvious reasons. What is it for something to be singular, or one?

The smallest whole unit.

It's fairly easy to see the differences between half a pig, a whole pig and two pigs.

What about one pair of pigs?

I'm afraid my answer would have to be the rather dry one (at least at first sight) that Frege was right about this, in sections 54 and 55 of his The Foundations of Arithmetic.

However, I find at least one crucial passage in section 54 obscure. In the second, long paragraph, after the main thesis of this section, which is that it would be a good idea to "call a concept the unit relative to the Number which belongs to it", he immediately goes on to try to make some sort of distinction between what might be called (although he does not use the terms) discrete and continuous concepts. Although I appreciate the need for some such distinction, I find his version of it unintelligible. (This admission may prompt me to have another go at understanding it.)

Section 55, defining (among other things) what it means for the number 1 to belong to a concept - he later goes on to explain that this does not yet define the number 1 as an object - raises (as does Russell's theory of definite descriptions) the question of what it means for two things to be "the same" or "equal" or "identical" - but let's leave that question for the thread with the title "The same"!

The smallest whole unit.

It's fairly easy to see the differences between half a pig, a whole pig and two pigs.