Do functions require constants? That is, can you have a meaningful function with only variables and no constants? I only ask because I've never seen a function without some sort of constant.
It's depended on the kind of the function. For example the Aria of a circle is a function of its radius and the number pi is a constant. A=(pi)*r^2
But there are a lot of functions that have only variables. For example the Identity function I(x)=x or Trigonometric functions, logarithmic ones , etc.
Thank you for the response. But even with exponential functions such as V(t)=Ke^t^1/2 you have a constant (K). And on wikipedia it says: Johann Bernoulli defined functions as any expression made up of a variable and some constants, and Leonhard Euler, during the mid-18th century, used the word to describe an expression or formula involving variables and constants. Also, in the function f(x)=x isn't there a 1 in front of the x?
you can argue that any f(x) in real/complex numbers is really 1*f(x) + 0, and therefore involves constants.
However, im pretty sure you could invent a number system where multiplication and addition didn't exist and still have function on that. In that case f(x)=x would not involve any constants.