Here are a few common misuses of technical words in writing and speech. While not using the terms correctly doesn’t necessarily mean a lack of understanding of the core concepts, the perception of your mastery of the concepts can be negatively biased by the side reading or listening to your (misspoken) words. Below are a few “favorites” that don’t make the usual list of “your/you’re”, “to/too”, “should of/should have”, etc..
Here’s how the color scheme works:
\(\checkmark\) and blue imply “good” use.
\(\times\) and reddish imply “bad” use.
deprecated vs depreciated
\(\checkmark\) What tags have been deprecated in HTML5?
\(\checkmark\) How should we depreciate our long-term assets for tax purposes?
\(\times\) What tags have been depreciated in HTML5?
Pronouncing Euler: Oiler vs Yuler
\(\checkmark\) If Euler were an Oiler then maybe we wouldn’t have used \(e\) for \(\sum_{k=0}^{\infty}\frac{1}{k!}\)
\(\times\) If Euler were a Yuler then he would have competed with Santa Claus.
L’Hôpital vs Le Hospital
\(\checkmark\) The H is “silent” and there is no “s” in L’Hôpital, which is pronounced [ lopi’tal ]. L’Hôpital’s rule was named after French mathematician Guillame François Antoine de L’Hôpital.
\(\times\) Joe English Speaker had appendicitis while he was in France. He kept asking that he be rushed to Le Hospital , but the French didn’t understand him and Joe died later that day.
A/An vs The
\(\checkmark\) It wasn’t me I tell ya! You’ve got a wrong guy! It was him over there! He’s the guy!
\(\times\) I’m sorry, you’ve dialed the wrong number.
A/An are indefinite articles and do not imply uniqueness. The is a definite article implying uniqueness. The cops didn’t get the wrong guy because that would imply that there was only one guy who was the wrong guy. The cops got a wrong guy. In the same way, saying that “you’ve dialed the wrong number” implies that there was only one wrong number to dial and that all other numbers dialed would have not been wrong. These distinctions are important in mathematics (and law). When asked to find the solution, we must also prove uniqueness in addition to existence. If asked to find a solution, we just have to show existence.
Admittedly, the common usage is “the wrong guy” and “the wrong number”.
Zero vs No Value
\(\checkmark\) The solution to \(x + 2 = 2\) is \(x = 0\). Zero is a value!
\(\checkmark\) There are no real values of \(x\) that satisfy \(x^{2} + 1 = 0\)
\(\times\) Since \(x = 0\), \(x\) has no value.
The notion of zero being a value can be a confusing one for those new to numbers. When people (typically children) are introduced to numbers, they are often given some type of context in terms of counting objects to understand what one is, two is, etc. That is there is one (1) apple. There are two (2) apples. When trying to conceptualize and contextualize zero, one apple is now replaced by emptiness. This can have a negative side effect of implying that zero represents non-existence. Elementary math instructors should take care here to explain the difference between the number of apples is zero and apples don’t exist.
Hyperbola vs Hyper Bowla vs Hyperbole
\(\checkmark\) \(\frac{x^{2}}{a^{2}} – \frac{y{2}}{b^{2}} = 1\) is a hyperbola [ hī-‘pər-bə-lə ] in \(x,y\) with \(a, b\) as positive constants.
\(\times\) A guy who throws spares and strikes and never a gutter ball, but drinks a lot of coffee and is from Boston is a hyper bowla.
\(\checkmark\) -“This is the best blog ever!!” -“Wow, that’s an exaggeration.” -“It’s not hyperbole at all. You’re here reading aren’t you?”
Axis/Axes vs Ax/Axe/Axes
\(\checkmark\) It’s the \(x\)-axis and the \(xy\)-axēs.
\(\checkmark\) To cut down a cherry tree a lumberjack would need an ax/axe. If there were more than one lumberjack, they would need as many axes (without a long “e”) as there were lumberjacks, otherwise the lumberjacks would have to take turns.
\(\frac{\sin(x)}{\cos(x)}\) vs \(\frac{\sin}{\cos}\)
\(\checkmark\) \(\frac{\sin(x)}{\cos(x)} = \tan(x)\)
\(\checkmark\) I went to the beach and got a tan.
\(\times\) I wrote \(\frac{\sin}{\cos}\) = tan on my trig exam.
Sine and cosine are functions that have one input (variable). Writing \(\sin\) or \(\cos\) or \(\tan\) (or any other function) is syntactically incorrect in mathematical writing. Such notation is, however, acceptable in a programming context when discussing these functions (methods if we are talking about member functions of a class).
Statistics: Accept the null hypothesis
\(\checkmark\) We reject the null in favor of the alternative.
\(\checkmark\) We retain the null.
\(\checkmark\) Though a double negative: We fail to reject the null.
\(\checkmark\) The court finds the defendant not guilty (fail to reject the null).
\(\times\) The court finds the defendant innocent (accepts the null).
Innocent is subtly different from not guilty. If a court finds a defendant innocent the implication is that there is a 0% chance that the person could have committed the crime he/she was accused of. A not guilty verdict simply states that there was not enough evidence to prove guilt, which is the alternative hypothesis . Thus, when conducting a statistical test, we will have a null hypothesis which we will ultimately (a) reject in favor of the alternative or (b) retain because of insufficient statistical evidence to the contrary. However, we will never accept the null.
Do you know of any other common misuses or mispronunciations of technical terms? Leave a reply!