Let's denote a total increasing computable function $f: \mathbb{N} \rightarrow \mathbb{N}$. How to prove that the plot of $f$ is a decidable subset of $ \mathbb{N} \times \mathbb{N}$?My solution:1) First of all, we consider a plot as a $X \times Y = \{ (x, y) | x, y \in X, Y \} \subset \mathbb{N} \times \mathbb{N} $. We know, if the function in monotone and total, it's actually bijective.So, my algorithm looks like this: we receive a pair $(a, b)$ and we want to check, if it belongs to $X \times Y$. So, we just calculate $f(a)$: if $f(a)=b$, we print 1, else we print 0.Could someone tell me, for what purpose the condition of the function'smonotonicity was added? 
Plot of a computable function
computability