clarification

Oleksandr Kulkov · adamant-pwn · commit 63cec1489737 · 2023-01-14T16:50:11.000+01:00
diff --git a/src/algebra/euclid-algorithm.md b/src/algebra/euclid-algorithm.md
@@ -9,11 +9,11 @@ e_maxx_link: euclid_algorithm
 Given two non-negative integers $a$ and $b$, we have to find their **GCD** (greatest common divisor), i.e. the largest number which is a divisor of both $a$ and $b$.
 It's commonly denoted by $\gcd(a, b)$. Mathematically it is defined as:
 
-$$\gcd(a, b) = \max \{k : k \mid a \wedge k \mid b \}$$
+$$\gcd(a, b) = \max \{k > 0 : (k \mid a) \wedge (k \mid b) \}$$
 
 (here the symbol "$\mid$" denotes divisibility, i.e. "$k \mid a$" means "$k$ divides $a$")
 
-When one of the numbers is zero, while the other is non-zero, their greatest common divisor, by definition, is the second number. When both numbers are zero, their greatest common divisor is undefined (it can be any arbitrarily large number), but we can define it to be zero. Which gives us a simple rule: if one of the numbers is zero, the greatest common divisor is the other number.
+When one of the numbers is zero, while the other is non-zero, their greatest common divisor, by definition, is the second number. When both numbers are zero, their greatest common divisor is undefined (it can be any arbitrarily large number), but it is convenient to define it as zero as well to preserve the associativity of $\gcd$. Which gives us a simple rule: if one of the numbers is zero, the greatest common divisor is the other number.
 
 The Euclidean algorithm, discussed below, allows to find the greatest common divisor of two numbers $a$ and $b$ in $O(\log \min(a, b))$.
 
