From 4bee68e6c4c7c60ada90bd6d01010621e0bd87c0 Mon Sep 17 00:00:00 2001 From: Jan Meyer Date: Tue, 28 Apr 2026 13:50:38 +0200 Subject: [PATCH] vault backup: 2026-04-28 13:50:38 --- 10 Courses/01 - WiSe 2025_26/DAS/Formulas.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/10 Courses/01 - WiSe 2025_26/DAS/Formulas.md b/10 Courses/01 - WiSe 2025_26/DAS/Formulas.md index 6289ca2..86657e4 100644 --- a/10 Courses/01 - WiSe 2025_26/DAS/Formulas.md +++ b/10 Courses/01 - WiSe 2025_26/DAS/Formulas.md @@ -1,6 +1,6 @@ ## Asymptotic Equivalence Classes (Big-O) -The equivalence relation definition given in the task is asking you to find functions that grow at the exact same rate (also known as Big-Theta $\Theta$): +The equivalence relation definition given in the task is asking you to find functions that grow at the exact same rate (also known as Big-Theta $Theta$): $f asymp g <==> f in O(g) and g in O(f)$ @@ -44,7 +44,7 @@ $$ &15^5 = 759,375 && "--- in the range / below" 10^6 \ &16^5 = 1,048,576 && "--- outside the range / above" 10^6 \ &=> 15 "numbers in the form "x^5"exist" && -$$ + > [!warning] > Now, we can't add $1,000$ and $15$, since there are numbers that match both, so we need to subtract these duplicates. @@ -54,6 +54,7 @@ $$ & 4^10 = 1,048,576 \ & => 3 "numbers that are both" x^2 "and" x^5 "exist" $$ + #### Final calculation: Formula: $"Elements that are" x^2 + "Elements that are" x^5 - "Elements that are both"$ $==> 1,000 + 15 - 3 = 1,012$