Quartz sync: Mar 1, 2025, 2:26 PM

content/Definitions/Sets/Complex Numbers.md

@@ -0,0 +1,6 @@
+$$z = a + ib$$
+$$z = r(\cos \theta + i\sin \theta)$$
+$$z = re^{i \theta}$$
+# Operations
+## Multiplying Vectors
+$$z_{1} \times z_{2} = (r_{1} \times r_{2})(\cos(\theta_{1} + \theta 2) + i \sin (\theta_{1} + \theta_{2}))$$

content/Definitions/Sets/Open Cover.md

@@ -0,0 +1,2 @@
+# Definition
+[[Open Sets]] with union $X$

content/Definitions/Sets/Open Map.md

@@ -0,0 +1,2 @@
+# Definition
+An **open map** takes one [[Open Sets|open set]] and maps it to another [[Open Sets|open set]].

content/Definitions/Sets/Open Sets.md

@@ -0,0 +1,4 @@
+# Definition
+An open set $A \subset X$ in $(X, d)$ (means set with a metric) consists only of [[Interior Point|interior points]].
+
+Then a sequence converges to $x \in X$ $\iff$ it eventually belongs to any [[Open Sets|open set]] containing $x$.