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.
We could use it like this in a family:
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.