ReallyBadAtMathGuy
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- Joined
- Nov 13, 2023
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We have to prove this inequality by induction for x > 0. Additionally, we have to conclude that |x| = ⌊log2 x⌋ + 1. I am struggling with the induction step as I don't know what to do
base case: x = 1
2|1| - 1 ≤ 1 < 2 |1| → 1 ≤ 1 < 2
induction step: x → x + 1
2|x+1| - 1 ≤ x + 1 < 2|x + 1|
→ 2|x| ≤ x + 1 < 2|x| + 1
Thanks for any help