- #1
shounakbhatta
- 288
- 1
Hello,
Can anybody tell me the meaning of
f:N^n -->N
Can anybody tell me the meaning of
f:N^n -->N
arildno said:It probably means a function whose domain is the n-dimensional set of natural numbers, and whose range is the (the 1-dimensional) set of natural numbers.
shounakbhatta said:For every function f: N^n -->N on the natural numbers, f is computable by an algorithm, f is computable by a Turing Machine.
What does it mean?
shounakbhatta said:Ok, understood.
Well, I have one question. In the Church Turing thesis, what is meant by a function?
Whatever we mean like y=f(x), in mathematics, is this a function?
You are right. It was a vague, unconsidered statement of mine in need of your precision. Thanks, Michael.Michael Redei said:What's an n-dimensional set? I think you mean the set of all n-tuples of natural numbers and the set of natural numbers itself, respectively.
The notation "f:N^n -->N" represents a function that maps a set of n-dimensional vectors, with elements from the natural numbers (N), to a single natural number (N). In other words, the function takes in a set of numbers and outputs a single number.
In this notation, "f" stands for the name of the function. It is a common practice to use the letter "f" to represent a function, but it can be any other letter or symbol as well.
The notation "N^n" represents a set of n-dimensional vectors, where each element in the vector is a natural number (N). So, "N^n" is essentially the input space for the function f.
The arrow in this notation represents the relationship between the input space and the output space of the function. In "f:N^n -->N", the arrow indicates that the function takes in a set of n-dimensional vectors and outputs a single natural number.
One example of a function represented by "f:N^n -->N" is the dot product function. This function takes in two vectors in R^n (where R is the set of real numbers) and outputs a single real number. In this case, the notation would be "f:R^n x R^n -->R".