Raised numbers are superscripts:
p
0 , p
1 , p
2 , p
3 , p
4
Lowered numbers are subscripts:
x
1 , x
2 , x
3 , x
4
In arithmetic and beginning algebra, superscripted numbers are exponents:
p
2 is "p squared"
p
3 is "p cubed"
p
4 is "4th power of p"
After introductory algebra, we see superscripts used for other purposes.
Subscripts are often used to distinguish items in a list from one another, according to some definition. This notation usually beings with algebra, but you can find examples elsewhere -- even outside of math.
A local hospital has multiple wings on most floors, and some executive decided to use the same room numbers in each wing:
356
1 means Room 56 Bed 1, on the third floor of the main wing
E356
2 means Room 56 Bed 2, on the third floor of the east wing
N356
4 means Room 56 Bed 4, on the third floor of the north wing
An example of subscript use in algebra is using symbols to represent values in a sequence (i.e., a list of ordered numbers). Here's one: powers of 2, begining with 2
1:
P = {2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, …}
P
4 represents the fourth number in the list (the 4th power of 2), so we can write
P
4 = 16
P
10 = 1024
Given P = 65536, you know it's a power of 2 but it's not clear which one.
Using symbol P
16 makes it clear that 65536 is 2
16.
We can also show superscripts and subscripts without special characters or formatting commands.
We use the caret symbol
^ and an underscore
_ .
P_16 = 2^16 = 65536
By the way, when I see notation like {P1, P2, P3} I think of subscripts.
