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--- tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2026/09/02 08:58] – [6. Lists] kissa
+++ tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2026/09/02 09:14] (current) – [7. Exercise] kissa
@@ Line 249: / Line 249: @@
 Reproduce the following mathematical proof in LaTeX. Use inline and display math, as well as basic and special symbols! Save the result in PDF format!
-{{:tanszek:oktatas:techcomm:pasted:20240902-144955.png}}
+{{:tanszek:oktatas:techcomm:pasted:20260902-091119.png}}
@@ Line 255: / Line 255: @@
 <code>
-Proof: √2 is Irrational
+Proof: 2 is Irrational
-Assume, for contradiction, that 2 is rational. Then it can be expressed as a fraction a/b, where a and b are coprime integers.
+Assumptions:
+Assume, for contradiction, that 2 is rational.
+It can therefore be expressed as a fraction a/b.
+a and b are coprime integers.
-Then:
+We can write:
-HERE COMES AN EQUATION.
+EQUATION
 Squaring both sides:
-HERE COMES AN EQUATION.
+EQUATION
 Multiplying both sides by b2:
-HERE COMES AN EQUATION.
+EQUATION
 This implies that a2 is even, so a must also be even. Let a = 2k for some integer k.
-Substituting into the equation:
+Substituting a = 2k into the equation:
-HERE COMES AN EQUATION.
+EQUATION
 Dividing by 2:
-HERE COMES AN EQUATION.
+EQUATION
 This implies that b2 is even, so b must also be even.
-But if both a and b are even, they are not coprime, which contradicts our original assumption. Therefore, 2 must be irrational.
+Conclusion: If both a and b are even, then they are not coprime.
+This contradicts our original assumption. Therefore, 2 is irrational.
 </code>