how do you show that for every set S, S ⊂ span S?

my working:

let S be the set of real numbers in n dimension.

then S = { x1,x2,...,xn l x1,x2,...,xn are real numbers}

then span S = a1x1+ a2x2+...+anxn

for all xi ∈ S, where 1<i<n

xi = a1x1+ a2x2+.+aixi+..+anxn iff all the coefficients are 0 except ai=1

thus xi ⊂ a1x1+ a2x2+.+aixi+..+anxn

can i prove this question like this? how should i define S since the proof requires that the statement is true for all S?

thanks