  This note develops an arbitrage theory for a discrete-time market model
without the assumption of the existence of a num\'eraire asset. Fundamental
theorems of asset pricing are stated and proven in this context. The
distinction between the notions of investment-consumption arbitrage and
pure-investment arbitrage provide a discrete-time analogue of the distinction
between the notions of absolute arbitrage and relative arbitrage in the
continuous-time theory. Applications to the modelling of bubbles is discussed.
