Some disambiguation is needed. There is some discussion of elements from the Chemistry perspective on the page about Atoms.
- A Periodic Table contains Elements
- The members of a Set may also be called Elements
This page concerns the elements of a mathematical set. We will provide simple explanations, assuming that this is your first exposure to the idea.
Identity Element
If we add zero to something, the result is the same.
5+0=5
Zero is the identity element for addition.
If we multiply something by one, the result is the same.
6*1=6
One is the identity element for multiplication.
Notice that we have to specify the operation (for our examples, addition or multiplication).
Inverse Element
If we add the negative of a number to a number, the sum is zero.
5 + (-5) = 0
For addition, the negative of a number is the inverse element that number.
- for +5, -5 is the inverse element for addition.
- for -5, +5 is the inverse element for addition
If we multiply a number by its reciprocal, the product is zero.
- For 2, 1/2 is the inverse element for multiplication
- For 1/2, 2 is the inverse element for multiplication
Notice that we have to specify the operation (for our examples, addition or multiplication).
Rob Sterling 