STEOP small quizzes: logic

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-known bias named "confirmation bias" (Nickerson, 1998). In this bias, we tend to look for confirmation or further support of some prior knowledge or experience, but we do not tend to look for counter-examples.

For example, what is the quick response that your brain comes up with for this problem:

This resource has been taken from the course on "Unconscious bias" developed at the University of Konstanz - to check the answer (and the entire course) see here.