The correct way to cancel scaling by a proportion is its reciprocal, ie, for x ≠ 0
x ∙ ¹⁄ₓ = 1
A 10% decrease is ⁹⁄₁₀
100% − 10% = 90% = ⁹⁄₁₀
Its reciprocal is ¹⁰⁄₉, a ¹⁄₉ = 11¹⁄₉% increase
1 / (100% − 10%) = ¹⁰⁄₉ = 100% + 11¹⁄₉%
We make it complicated by stating increase/decrease & percent instead of simple scaling factors.
The western world has a weird 💯 fetish almost as funny as ancient mesopotamians and the number 60.
In general, for proportional change x, the proportional change y to cancel it is the solution of
Just noticed if you also decrease something by 10%, then increase by 10%, you also get a net loss of 1. Math itself is biased towards loss.
Anyone convinced in the malevolent creator theory yet?
Math isn’t biased. Flawed reasoning is. For x ≠ 0
The correct way to cancel scaling by a proportion is its reciprocal, ie, for x ≠ 0
A 10% decrease is ⁹⁄₁₀
Its reciprocal is ¹⁰⁄₉, a ¹⁄₉ = 11¹⁄₉% increase
We make it complicated by stating increase/decrease & percent instead of simple scaling factors. The western world has a weird 💯 fetish almost as funny as ancient mesopotamians and the number 60.
In general, for proportional change x, the proportional change y to cancel it is the solution of
Increase by 10 then decrease by 10. Same problem. Math is lossy.
Adding flat numbers is different from adding a percent.