So I added this to the Wikipedia definition:

> Note: There is a further technical condition that \$$\phi^t\$$ is an action of T on M. That includes the facts that \$$\phi^0\$$ is the identity function and that \$$\phi^{s+t}\$$ is the composition of \$$\phi^s\$$ and \$$\phi^t\$$. This is a semigroup action, which doesn't require the existence of negative values for t, and doesn't require the functions \$$\phi^t\$$ to be invertible.