Set Theory Functions: SUBSCRIPTION

So, how do we extract an element from a set? We simply subscribe them.

SUBSCRIPTION is represented by a number that is, in font terms, subscripted from the font. For example, S₂.
The number scheme is undefined for sets, but usually, the first element is represented by the number 0.

Subscription can take on two parts, one is to subscribe by the index and the other is to subscribe by the symbol name.

SUBSCRIBING BY INDEX

Subscribing by index means you want to get a symbol based on its position in a set.
For example, S = {a,b,c,d}, we want symbol c. We see that it is in the third position, so S₃ = {c}.
Sometimes the index is a variable. So not to confuse it with a symbol name, if the index is a variable, it is italicised, for example x is the index. So the xth index of S would be S_x.


SUBSCRIBING BY SYMBOL NAME

Subscribing by symbol name means you want to get a symbol based on its name.
For example, S = {a,b,c,d}, we want symbol b. To get b, we just specify it in the subscription, so S_b = {b}.

Subscription can be used with the other functions. Say we want to remove all elements with index 3 and S = {a,b,c,d} We would do S\S₃ = S\{c} = {a,b,d}.
To unite a subscripted factor, say we want to unite one set and the third element of another set. S = {a,b,c,d} and J = {e,f,g,h,i}. S UNION J₃ = {a,b,c,d} UNION {g} = {a,b,c,d,g}.