# Are Arithmetical Truths Empirically Falsifiable?

It is crucial to understand the difference between two kinds of mathematics to really understand the question of arithmetical truths being empirically falsifiable or not. These two contexts in which we can analyze mathematics are pure mathematics (imaginary world) and applied mathematics (the real world around us). The imaginary world is the world that is created by formulas and mathematicians to try to understand the world in a general matter with certain theories while applied mathematics deals with real world problems rather than going for a general explanation. We can make this distinction by saying that pure mathematics never really only deals with the real world when it is applied thus causing it to be used as applied mathematics. Thus pure mathematics to a point is the cause for applied mathematics but this does not mean that pure mathematics deals with real world problems but rather might be the answer to some of the problems in the real world.

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