This research paper will examine the differences between the ideas of impossibility of Alain Badiou and Slavoj Žižek from their readings of the French poet and critic Stephane Mallarmé. The discussion will focus on how Badiou and Žižek diverge in their respective interpretations of the impossibility as a hallmark of the Lacanian Real in Mallarmé's work. This difference is framed in the way in which Badiou and Žižek draw on their ideas with the modernist poet Mallarmé to understand the conditions under which the subject can try to access this imperative idea. Here it will be shown that this two relationships become apparent: subtraction and purification; subtraction as the elimination of the imaginary contents of the subject's self-relationship in an attempt to access the future antierieur and purification as the attempt to purify the pure idea by locating the opaque core of the aesthetic ob