What do these small numbers like powers but are below mean?

Question

I have encountered those small numbers that are like exponents but are beneath numbers instead of above. What do they Mean?

$$x_1,x_2,\ldots,x_n$$

Such subscripts just distinguish values. $x_1$ has some value, $x_2$ has some value. You could instead use $a$, $b$, $c$, but that gets ugly. — David G. Stork, Sep 08 '20 at 20:05

user · Accepted Answer · 2020-09-08T21:06:45.970

5

These are indices to distinguish the variables $x_i$ with $i=1,2,\ldots,n$.

They are often used for example in multivariable calculus and linear algebra when we deal with more than $2$ or $3$ variables as an alternative to $x$, $y$, $z$, etc.

edited Sep 08 '20 at 21:06

answered Sep 08 '20 at 20:08

user

154,566

1

Thanks for the simple And straightforward Answer!! – Mohamed Technology Sep 14 '20 at 11:19
You are welcome! Bye – user Sep 14 '20 at 11:23

score 2 · Answer 2 · answered Sep 08 '20 at 21:06

In addition to other good answers, sometimes "$x$" denotes a vector in $n$-dimensional space, and "$x_i$" is the $i$-th component of it, written as an $n$-tuple: $x=(x_1,x_2,x_3,\ldots,x_n)$.

Also, sometimes $x_1,x_2,\ldots$ is a sequence of values that a variable $x$ can take.

Sometimes, $x_1$ and $x_2$ are names for the two solutions to a quadratic equation in the "variable" $x$...

Basically, though, unlike superscripts (=exponents), subscripts mostly do not denote any standard operation on the variable to which they're attached. In the vector case, this is so, if we want to interpret it that way... but, still, not really.

score 1 · Answer 3 · answered Sep 08 '20 at 20:57

1

Each of them is called an index (plural: indices) or, rarely, subscript. See e.g. https://en.wikipedia.org/wiki/Index_notation

answered Sep 08 '20 at 20:57

Torsten Schoeneberg

26,051

What do these small numbers like powers but are below mean?

3 Answers3