Just out of curiosity

Let's apply what we learned about logic to some particular scenarios: Definition: we say that a sequence \((x_n)_{n\in \mathbb{N}}\), \(x_n\in \mathbb{R}\) converges to \(x\in \mathbb{R}\) when for all \(\varepsilon>0\) there exists a \(N\in \mathbb{N}\) such that for all \(n\geq N\) it holds that \(|x_n-x|<\varepsilon\) Definition: we say that a function \(f: \mathbb{R}\to \mathbb{R}\) is continuous at \(x\in \mathbb{R}\) when for all \(\varepsilon>0\) there exists a \(\delta>0\) such that if \(0<|y-x|<\delta \), then \(|f(y)-f(x)|<\varepsilon\).  Quiz: Write the negation of these definitions, i.e., what does it mean that a sequence \((x_n)_{n\in \mathbb{N}}\) DOES NOT converge to \(x\in \mathbb{R}\), and what does it mean that a function \(f: \mathbb{R}\to \mathbb{R}\) is NOT continuous at \(x\in \mathbb{R}\).  Cognitive bias We have many cognitive biases, which include biases on how we think about things. For example, there is a well-kno...