Generally speaking,a strategy Ψ is said to be an arbitrage if it makes something out of nothing without risk,i.e V_T(Ψ) is strictly positive with positive probability and with its initial wealth 0.If the net capital gains are strictly positive with positive probability,we can't tell whether it is an arbitrage.How do you tell whether a strategy is an arbitrage with its initial wealth unequal to 0? We give another definition of arbitrage and have shown that judging whether a strategy is an arbitrage is to judge whether its discounted gains are strictly positive with positive probability. We give the equivalent expression forms in mathematics of the original market and different discounted markets with respect to no arbitrage ,and correspondingly we get equivalent expression forms in mathematics with respect to no arbitrage with different strategy requirements.