> If the annual increase is capped at 2% and inflation is >2% then the value reaped by property tax will eventually go to 0.

Asymptotically at infinity, you're not wrong.

I'm probably not living that long though. Meanwhile taxes do go up every year in real money.

Taxes go up in nominal money :)

Can't they game their way around that though by just increasing the assessed the value of the property? That's how my town effectively raises property taxes beyond the statutory limits. Sure you can appeal the assessed valuation but most people don't. It is expensive and time-consuming.

It’s fixed at the original assessment the last time it was sold, I think. It also applies to businesses, with the result that the car dealership next to me pays less taxes than a new condo. Inheritance does not reset it, meaning the state is effectively living under feudalism.

There was an attempt to fix this for businesses just last year, but it failed because homeowners were convinced it was a plot to get them.

No, it's fixed at when the house was built. You'll see "renovations" where the entire house minus one wall is demolished, and the new structure built around it. This allows the owners to avoid reassessment.

and if inflation is under 2% and the city always increases by the maximum of 2%, then eventually the value of the property tax paid will be infinite, right? How is that analysis useful?

If you make property tax a fixed percentage of the value of the property, it automatically adjusts with inflation.