finite set

[plush needle]

Can I assume S is finite here?

[obtuse fox]

What is the definition of linear independence that you are familiar with ?

[plush needle]

if a1x1+a2x2+...anxn = 0, then a1, a2, ...an are not all 0

[cyan shuttle]

It should be that they are all 0 then, right?

[cyan shuttle]

Anyway, in one direction: If $S$ is linearly independent and $T\subseteq S$ is finite, I think you can easily show that $T$ is linearly independent.

In the other direction, try the contrapositive. Suppose that $S$ were not linearly independent. What does that imply exists? Use this to find a finite subset $T\subseteq S$ which is also not linearly independent.

[empty stratus]

Pear Category Theorem

[plush needle]

yeah

[plush needle]

@cyan shuttle whatabout this

[cyan shuttle]

Not unless the problem says you can. But you also do not need to assume that.

[plush needle]

so it's possible that S has infinite finite subsets right

[spare arrow]

@plush needle

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