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2.7 Powers and roots

There are several symbols for powers and roots: for instance, 24 means ‘2 to the power 4’. An alternative to 24 is 24, where the symbol Author(s): The Open University

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2.6.2 Try some yourself

1 Read the following expression out aloud or write it out in full in words:

  • (a) 3 × 4 + 3 × 5 = 3 (4 + 5).

Answer<
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2.6.1 Arithmetical symbols

You will have already met the symbols for the basic arithmetical operations, which are +, −, × and ÷, but you may not have met some of the alternative ways of writing × and ÷.

To recap, the main symbols for arithmetical operations are:

There are other alternati
Author(s): The Open University

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2.5.1 Try some yourself

1 How would you add the following words to the list:

 decimal, fraction, positive, negative.

For each one, give the mathematical meaning and an example of its use.

Author(s): The Open University

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12 Dividing decimal numbers by moving the decimal point

Doing division when decimal numbers are involved is the same as doing divisions involving whole numbers, with a few extra steps to take care of the decimal point.

Either the number you are dividing into or the number you are dividing by, or both of them, may be a whole number or a decimal number. So, for example, you might want to do the following divisions:

  • Example 1: 49.26457 ÷ 8
  • Example 2: 2.601 ÷ 1.22
  • Example 3: 678 ÷ 27.3
    Author(s): The Open University

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5.3 Neighbourhoods

We know that a polygon X is a surface and so each point x in X has a disc-like or half-disc-like neighbourhood. We shall show that a map f that identifies edges of a polygon to create an object Y automatically creates corresponding disc-like or half-disc-like neighbourhoods of each point y = f(x) of Y.

If x is in the interior of X, there is no difficulty: the point x has a disc-like neighbourhood U
Author(s): The Open University

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2.4.1 Remarks

  1. This theorem applies to all surfaces and not just to surfaces in space.

  2. This theorem tells us that the boundary number is a topological invariant for surfaces, i.e. a property that is invariant under homeomorphisms.

  3. It follows from the theorem that two surfaces with different boundary numbers cannot be homeomorphic. It does not follow that two surfaces with the same boundary number are homeomorphic –
    Author(s): The Open University

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