B Are there really 4 fundamental math operations?

[rootone]

What if a can be derived from b, which can be derived from c, and c can be derived from a. What is fundamental there?

My guess would be that a,b, and c are the same thing and the distinction depends on the state (or choice maybe?),of the observer.

 

[_PJ_]

What if a can be derived from b, which can be derived from c, and c can be derived from a. What is fundamental there?

Unfortunately, there can be many definitions of the term “fundamental”.

No. I must disagree; there is one definition of fundamental.

In your ecample, neither a nor b nor c are fundamental

I fear this discussion heading into murky waters of Kurt Gödel :)

Maybe nothing is fundamental, and mathematics is a magically stable house of cards on a foundation of imagination supported by matjematical elephants!

 

[rootone]

The concept that if I have two apples, and I will give one to you if you give me an apple back tomorrow seems like a fairly safe axiom.

 

[pwsnafu]

Surely if something is derived (or can be derived) from another, then this rules out that something as a fundament and may enforce the 'fundamentality' of the other.
¿?

If that's your definition of fundamental, then addition of natural numbers is not fundamental. We define addition as $a+S(b) = S(a+b)$ where $S$ is the successor operator.

 

[_PJ_]

If that's your definition of fundamental, then addition of natural numbers is not fundamental. We define addition as $a+S(b) = S(a+b)$ where $S$ is the successor operator.

who's "we" and why is the current mode of pregerred definition assumed to have any real objective arbitration over the nature of fundament?

I'm not arguing- I fully appreciate your most certainly more quaölified expertise - only I don't believe that answers to such questions can be so definite or absolute.
I have on reflection, changed my premature mindset concerning addition already since my first post in this topic, though.

 

[_PJ_]

incidentally, please be awate that in the quoted, tecent post, I made no cöaim as to what my definirion of fundamental was, only provided one example of what it clearly ISN'T.
There's a huge difference

 

[Baluncore]

No. I must disagree; there is one definition of fundamental.

I agree that there can be only one definition in anyone field. But here we are discussing multiple different fields. Mathematics requires internal consistency, while a post-modernist analysis allows for many interpretations in many different fields, or schools of thought. For example; teaching arithmetic to children, or the assumptions that underly formal mathematics.

 

[newjerseyrunner]

I think what is fundamental depends on context. For example, you say that you can't derive addition from more fundamental functions.

I can do binary integer addition with XOR, AND, and SHR . To me, there are three fundamental operators: AND, OR, and NOT.

So you can define your own axioms given your specific domain. If your domain is integers, then addition is the only axiom. If you're representing your integers as binary strings, addition is derived from more fundamental logic.