 The two acts of intuitionism form the basis of Brouwer’s philosophy; from these two acts alone Brouwer creates the realm of intuitionistic mathematics, as will be explained below. Already from this basic principles it can be concluded that intuitionism differs from Platonism and formalism, because neither does it assume a mathematical reality outside of us, nor does it hold that mathematics is a play with symbols according to certain fixed rules. In Brouwer’s view, language is used to exchange mathematical ideas but the existence of the latter is independent of the former. The distinction between intuitionism and other constructive views on mathematics according to which mathematical objects and arguments should be computable, lies in the freedom that the second act allows in the construction of infinite sequences. Indeed, as will be explained below, the mathematical implications of the second act of intuitionism contradict classical mathematics, and therefore do not hold in most constructive theories, since these are in general part of classical mathematics.