the point of the example was to illustrate how people fixate on the increased cost of living fron inflation and ignore their increased earnings, even if the increased earnings out-pace the inflation in their cost of living. my point is that's a bad example because we couldn't say that that's true given that the cost od living has been out-pacing wage inflation for a long time.
so yeah, the example illustrates the idea, but it also underlines how the idea contradicts reality.
No, the point of the example was not to make any specific claim about wages or inflation. The point of the example was to illustrate that wages and inflation are relative. That's it.
If instead OP had said "if wages go up 500%, and prices go up 1,000%, everyone is worse off and got a 500% pay cut", then the main point being made would remain exactly the same. Again, this is because the exact numbers were never relevant, and the example was for explanation purposes.
Now apart from the fact that we are now 6 comments deep in the most pedantic thread I have ever had the displeasure of participating in (this is my fault too, to be fair), you also might be interested to know that cost of living/inflation has not outpaced wages for a "long time" as you so claim.
Here's a graph from the last 30 years, for example, showing earnings keeping up with inflation.
https://fred.stlouisfed.org/graph/?g=iuyN
Or maybe you'd just like to look at more recently, in which case, looking at just the past year, wages have still kept up.
https://usafacts.org/answers/are-wages-keeping-up-with-infla...
Or if your a low wage earner, those wages have especially kept up, outpacing inflation and even high wage earners by significant margin in recent years.
https://www.epi.org/publication/strong-wage-growth-for-low-w...
This is not to say that there is no affordability problem, but no matter what way you put it, your specific claim, that wages have not been outpaced by inflation "for a long time", is demonstrably false.