**Definition:** Let $I \subset k[x\_0,\ldots,x\_n]$ be a homogeneous ideal (or a set of homogeneous polynomials). 
The set $Z(I) := \{(a\_0 : \cdots : a\_n)\in P^n ; f(a\_0,\ldots,a\_n) = 0 \ \ \forall f \in I\}$

Subsets of $P^n$ that are of the form $Z(I)$ are called algebraic sets. If $X \subseteq P\_n$ is any subset, we call $I(X)$ the ideal generated by
$\{f ∈ k[x\_0,\ldots,x\_n]: f \ \text{ homogeneous},\ f(a\_0,\ldots,a\_n) = 0 \forall (a\_0 : \cdots : a\_n) \in X\}$; by definition this is a homogeneous ideal.

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> > A remark that is sometimes useful is that every projective algebraic set can be written as the zero set of finitely many homogeneous polynomials of the same degree. 
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While studying projective varieties, I read the above remark in the box. I dont understand this remark, please how to show this remark clearly. I want to learn its proof. Thank you for helping.