L’Hôpital’s Rule: What and Why
The next few posts will look at a powerful technique for finding limits in calculus, called L’Hôpital’s Rule. Here, we’ll introduce what it is, and why it works. In the next post we’ll examine some harder cases.
Month: February 2019
Patterns of Logical Argument
We’ve looked at various aspects of turning English sentences into logical statements, and modifying them by negation, converse, and so on. Let’s finish by looking at some questions about standard rules of inference, such as Modus Ponens and the Law of Syllogism.
Complicating the Converse
(An archive question of the week) Usually when we discuss converses (and inverses and contrapositives) we use clear, idealized examples. But statements in real life — even in real math — are not quite so straightforward. The difficulty is not merely in the language, but in the complexity of our statements. A question in the …
Converse, Inverse, and Contrapositive
This is the third post in a series on logic, with a focus on how it is expressed in English. We’ve looked at basic ideas of translating between English and logical symbols, and in particular at negation (stating the opposite). Now we are ready to consider how to change a given statement into one of …
Negating Logic Statements: How to Say “Not”
Last time, I started a series exploring aspects of the translation of English statements to or from formal logical terms and symbols, which will lead to discussions of converse and contrapositive, and eventually of logical arguments. We’ve looked at how to translate concepts of “or” (disjunction) and “if” (conditional); but our goals will also require …
Translating Logic Statements
The next few posts will examine aspects of logic, both symbolic logic, and how we talk about theorems in general. We’ll start here with issues in interpreting the wording of logic, and some of the semantic difficulties we face. English isn’t logical. (Well, I suppose humans in general aren’t logical.)
Significant Digits: Measurements and Exact Numbers
To conclude this series on significant digits, I want to look at some details of their application. Specifically, we will consider questions about how they related to measured values, and to fixed constants.
Significant Digits: Digging Deeper
We’ve looked at the basic concept of significant digits, then at how they interact with operations, which is one reason for defining them. This time I want to look a little closer at why they are defined as they are, which will involve considering some special cases.