I am reading about matroids and I am kind of confused in the following definition.
A nonempty subset $C$ of $\{0,1,...,n\}$ is a circuit of $I$ if $C= supp(l)$ for some nonzero linear form $l$ in the ideal $I$, and $C$ is inclusion-minimal with this property.
The part I am confused about is the inclusion minimal part. Could someone give me an intuition or example that shows this idea?