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Yearly archive for 2014.


Dear Professor Puzzler,

What is the difference between the words "compliment" and "complement"? Do they mean the same thing?

From, Lizzie in Sacramento


Dear Lizzie,

The word "compliment" is what you call it when someone says something nice about someone. The word "complement" is used to describle something that completes something else. In mathematics, "complementary" is used to describe angles that add up to a right angle when put together. You may also hear the term "complimentary" used to describe something, and that generally means it is something that is free, in other words, given "with our compliments."

  • Megan gave me a very nice compliment about the color of my earrings.
  • My spouse and I complement each other very well.
  • We greatly enjoyed the complimentary breakfast at the hotel this morning.


Professor Puzzler


What's the difference between an adjective and an adverb?



Hi Wallace,

First, let's talk about how adjectives and adverbs are alike, then we can talk about how they're different.  Adjectives and adverbs are parts of speech, and they are both words that are used to describe other words.  For example, if you say "That's a good question," good is a describing word, so it's either an adjective or an adverb.  Can you find the describing words in the following sentences?

  • I ran very slowly.
  • I saw a blue balloon.
  • The extraordinarily ugly monster ate the burnt toast.

How did you do?  In the first sentence, "slowly" is a describing word; it describes how you were running, and "very" is also a describing word, because it helps to explain just how slowly you were running.  In the second sentence, "blue" is a describing word, and it describes the balloon.  In the third sentence, there are three describing words: "extraordinarily," "ugly," and "burnt."

Now let's talk about how adjectives and adverbs are different.  The difference can be described quite easily as follows: if a word is describing a noun, it is an adjective.  If it's describing anything else (a verb, an adjective, or another adverb), then it's an adverb.

So, with that in mind, can you go back through those three sentences above and determine which are adjectives, and which are adverbs?

Here are the answers:

  • adjectives: blue, ugly, burnt
  • adverbs: very, slowly, extraordinarily

By the way, sometimes people will tell you that you can recognize adverbs because they end in "ly," but that's not always true.  For example, in this sentence, always is an adverb, but it definitely doesn't end in "ly!"

I hope that helps, and thanks for asking!
Professor Puzzler



Hi Professor Puzzler, I was wondering if you could explain what an axiom is?

Katie M, Grade 11
South Dakota


Hi Katie,

Well, I'm guessing that you're taking a Geometry class, because that's when many students first see that term.

An axiom is something that you believe or accept to be true without having ever proven it.  It is something that you consider to be "obviously true." You might not realize it, but your life is filled with axioms - things that have never been proven to you, but you believe anyway.  I once asked a group of high school students to name some things they couldn't prove, but they were confident of anyway.  Here were some of their answers:

  • My parents love me.
  • The sun will rise tomorrow.
  • Gravity keeps me from falling out into space.
  • There is a God.
  • 1 + 1 = 2.

Why are axioms important? Because when you are proving something, there will always be fundamental building blocks of ideas that your proof is based on, and it's important to remember that the most fundamental building blocks are actually things you haven't proved at all.

In a way, an axiom is sort of like what the Bible says about faith: faith is the substance of things unseen.

Euclid had some axioms (or postulates), and one of his very important axioms was that if you have a line, and a point that's not on the line, there's only one line that goes through the point, and is parallel to the line.  That might seem obvious, but some other mathemeticians like Lobachevsky, Riemman, and Gauss had some different ideas, and their notions of geometry turned out to be very different from Euclid's.

The assumptions you start with can drastically change your results!

In modern usage, the "obviously true" concept is not how axioms are always viewed; in another sense, we could view an axiom as simply a "rule of the game" in mathematics.  In other words, mathematicians might say, "Let's start from assumption X, and see what sort of mathematics we develop!"  The assumption, or axiom they begin with may not be something that's "obviously true," but often valuable results come from such game playing.

Thanks for writing,
Professor Puzzler


Please explain the difference between the words "they're" and "their."

Andy K.
Grade 5


Hi Andy,

The answer isn't too complicated.  The word "their" is a possessive word.  That means that it shows that someone owns something.  In this case, it means that something belongs to a group of people (them). 

  • They brought their car to the repair shop.

"They're" is a contraction of "they" and "are".  

  • They're having car problems.

Here is a sentence that contains both words:

  • They're hoping that their car will be fixed soon.

Thanks for asking!
Professor Puzzler

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