**Inverse**[or

**Inverted]**and

**Recur [**or

**Recurring]**. Let's invert the order and define

**Recur**first, okay?

*(Is this a clever way to define inverse, or what?)*

**Recurring**means

*continuing, on-going, repeating repeating repeating*.

In math we could use it like this:

Give the value 2/3 in decimal form. Answer = .66666666 In this case, the 6 is a recurring number.

Dave and Katy had a recurring argument over the size of Katy's mobile phone bill!

Or like this:

In her recurring dream, she would always have to give a speech to a large group of people ...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now let's get back to

**inverse**. It means

*turn over; opposite; reverse, negative, "the other way".*

In math, we can use it like this:

Give the inverse of the fraction 2/3: Answer = 3/2 Another term for this is

**reciprocal**.

Notice that the product [

**multiplicative inverse**] of these two numbers is one. That means zero can't have a reciprocal, because 0 times a real number is 0, not 1.

Or we can use inverse like this:

Give the inverse of the real number -5: Answer = 5

Notice that the sum [

**additive inverse**] of these two numbers is always zero.

This discussion has reminded me of two more words that we sometimes use in the math curriculum - most often describing coins. These are

**obverse**and

**reverse**.

**Obverse**means

*turned to face you.*

**Reverse**means

*turned to face the other way*.

We would use it like this:

Which side of a coin is the obverse? The face or "heads" is always the obverse side. In the case of coins without a portrait (the Euro) the obverse is the common side, shared by all variations of the coin.

Which side of a coin is the reverse? The back side or "tails" is always called the reverse.

These photos show a Roman coin that my friend Ken located in a field in Dorset, England. He gives most of them to the farmers who own the fields, or to museums.

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