Through Martin Heideggers critique of the traditional metaphysical understanding of temporality the relationship between the infinite and finite has been set in a new light. Heidegger emphasizes that the human being only inheres in the realm of finitude, but, in his debate with Ernst Cassirer at Davos in 1929, he says that the human being has a certain infinitude in her ontological understanding of being. In this essay I aim to explore the possibilities of this statement by showing how the finitude of Dasein is only finite in respect to an infinite horizon, as in the metaphysical understanding of the temporal existence as rooted in an atemporal essence, but that Heideggers concept of finitude must be understood as a kind of infinite finitude.