Indeed, and modern economics as a discipline goes out of its way to keep everything finite. I was going to post the same thing: that the finite version solves

Indeed, and modern economics as a discipline goes out of its way to keep everything finite. I was going to post the same thing: that the finite version solves this problem completely. The only case where economics cannot avoid dealing with infinite quantities, is with dynamic issues, since most models assume that various quantities though finite at a given point, could grow without bound (e.g. GDP). One case this comes up is in debt, especially national debt. Most models posit a transversality/"no ponzi" condition, that states that the present value of debt at time t will converge to zero as t goes to infinity. On the other hand, if national debt was a constant proportion of GDP (which in the long run should grow at the same rate as the risk free interest rate) then this would in fact be false, and national debt is a kind of free money that comes out of nowhere, i.e. a real ponzi scheme. Imposing a finiteness condition (e.g. and end to the universe) would imply that in the far future, some generation will pay for current consumption that is based on either national debt, or the corresponding internal borrowing from future generations (e.g. social security as understood in the overlapping generations model). That is why, in my opinion, it is completely wrong to say that household finances don't apply to government. The only difference is the kind of consumption and investment being done, but the financial constraints are identical.