Inversion

Date: 2025-09-02 AO: 3rdf-timekeeper Q: bratwurst PAX: frasier, madison, citgo, Gump FNGs: None COUNT: 5 Part 1 – Start by assuming the statement is either true or false, then explore what else must be true to make it so.
Example 1: Business Strategy
Claim to Prove: “If we reduce customer churn, revenue will increase.”
1. Assume the claim is true.
For revenue to increase, it must also be true that:
The cost of retaining customers is less than the cost of acquiring new ones.
Retained customers either keep buying or increase their purchase volume.
Competitors don’t simultaneously pull customers away faster than we retain them.
2. Test the assumptions:
If these hold, reducing churn does lead to higher revenue.
If they don’t, reducing churn alone may not guarantee revenue growth.
✅ Inversion shows that the claim’s truth depends on underlying business conditions, not just the churn metric.
Example 2: Personal Decision-Making
Claim to Prove: “Exercising three times a week will make me healthier.”
1. Assume the claim is true.
For this to be true, it must also be the case that:
The exercise chosen actually improves cardiovascular or muscular health.
Nutrition, sleep, and recovery aren’t neglected.
The exercise frequency is sustainable and doesn’t cause injury.
2. Test the assumptions:
If these hold, then exercising three times a week leads to better health.
If they don’t (e.g., exercising but also smoking heavily), the claim may fail.
✅ The assumption reveals hidden conditions that determine whether the action (exercise) achieves the desired outcome (health).