Yes. Since ##\mathbb{Z}_2## is a field everything is fine in ##\mathbb{Z}_2^n##, the ##n-##dimensional unit cube.entropy1 said:Could you view a discrete number, for instance a binary number, as a sort of orthogonal basis, where each digit position represents a new dimension? I see similarities between a binary number and for instance Fourier Transform, with each digit being a discrete function.
A basis in binary numbers refers to the set of numbers used to represent values in the binary number system. In binary, the basis is made up of two numbers, 0 and 1, which are used to represent all other numbers.
To determine if a number is a basis in binary, you must check if it is composed of only 0s and 1s. If it contains any other numbers, it is not a basis in binary. Additionally, a number must be able to represent all other numbers using only 0s and 1s in order to be considered a basis in binary.
No, a number can only be a basis in one number system. For example, the number 2 is a basis in the decimal number system, but it is not a basis in the binary number system.
The binary number system uses a base of 2, which means there are only two possible digits to represent all numbers, 0 and 1. This is because in binary, each digit's value is determined by its position in the number, rather than the actual value of the digit itself.
The basis in binary numbers is significant because it allows us to represent and manipulate numbers using only two digits. This makes it easier for computers to process and store data, as they use binary code to represent and communicate information.