wait until you learn about Ackermann
The article is about extending the domain of the ackermann function
The Fourth Operation: What Comes After Exponentiation
51–54 of 54 posts
Re: The Fourth Operation: What Comes After Exponentiation
#52Earlier quoted context omitted.
Multiplication outside of positive integers is not "repeated addition". It took us thousands of years to properly define real numbers. High school students can live without a perfect explanation, or we can just teach limits before college since they are the fundamental concept if calculus.
To clarify where I live limits are introduced in high school, irrational numbers just much earlier.
Multiplication is repeated additions is the informal way of stating the distributive property of multiplication and addition.
Probably you were taught how to multiply irrational by the property of powers (a^b * c^b = (a*c)^b etc.).
You were not taught a grand unifying theory of multiplication, you were taught how to manipulate operations to turn them into more useful operations.
Teaching these laws also prepares you for when a and b are just symbolic reals with no structure and those laws are the only thing you can use to manipulate them.
Re: The Fourth Operation: What Comes After Exponentiation
#53If addition is "the first operation", then "increment" is the zeroth operation. You know, counting 1,2,3,4. If we define multiplication as repeated addition, then we define addition as repeated increment, where A + B is: start at zero, increment A times then B times.
increment is no longer a binary operation
Re: The Fourth Operation: What Comes After Exponentiation
#54Are you aware whether this function is analytic?