Describe the structure of the Real Number System, defining each type of number which it comprises and making clear the relationship between them.
The first numbers that we are introduced to from an early age are 1, 2, 3, 4 etc.
These are called the 'Natural numbers', and can be placed on a number line from 1
to infinity. The natural numbers, in order, are always 1 whole number larger or
smaller than the next.
When we add or subtract the natural numbers the answer is always a natural
number. If we use subtraction or division however, we would without any other
system, not always be able to obtain an answer within the natural number system.
The sum 8 minus 10 for example would be impossible therefore a new number
system is needed. Suggate (1998, p.40) uses temperatures below freezing as an
example. In this instance we record how many degrees below O°c it is by counting
backwards from 0, to the left, using the 'negative' numbers. The integers are all
positive and negative whole numbers including 0 but the positive integers are also
When taking into account these numbers it is not always possible to calculate while
keeping the sum within the integer system. Therefore another system is needed. If
we take for example 1 cake which is whole and divide it into 4 parts. Each piece is
considered ¼ of the original whole cake. Therefore there are 4 ¼ pieces. These
fractions or 'rational numbers' tell us this by the bottom numbers - the denominator.
The number on top of the fraction is the numerator and tells us about how many
parts we are dealing with. With fractions there are different ways to write the same
amount, e.g. 2/4 is equal to ½ . However we can also write fractions as decimals.
Therefore ½ , half a whole number, can be expressed as 0.50 ( a half of 1)...
... fraction. Since i is not a rational or irrational number, then it is also NOT a real number. The English language can lend itself to be used for other purposes. When you first heard about a white lie you were thinking ... for other purposes. When you first heard about a white lie you were thinking about it using the English way only (because it has nothing to do with mathematical or scientific description), but with an imaginary number you could think of ...
... just subtract 1. This means all its powers are just whole multiples of itself plus another whole integer (and guess what these whole integers are? Yes! The Fibonacci numbers again!) Fibonacci numbers are ...
... of sizes of sets. They do not model sizes of sets the way that natural numbers do. If you say "I ate 3/4 of a pie", you are ... they are not really imaginary at all. (The name dates back to when they were first introduced, before their existence was really understood. At that point in time, people were ...
... known for a series of numbers which we call Fibonacci numbers. Fibonacci numbers are a sequence of numbers that, except for the first number, are ... many nations' flags is a product of that ratio. But Fibonacci numbers also appear in nature. For example, the spiral arrangement of seeds in a sunflower ...
... uncountable infinity of properties of natural numbers to ... 1. The celebrated Goodstein sequence results by repeated bumps and subtractions of 1, starting with some ordinal, finite or infinite. The ...
... daisies. In many cases the leaf arrangement is related to maximizing space for each leaf. "So nature isn't trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the ... flowers are shaped they way there are, but here Fibonacci has explained one way in how flowers are created. Sources Knott, Robert. Fibonacci Numbers and Nature. http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html Scientific Mysteries: Fibonacci ...
... Catalan Numbers, Natural numbers, Pentatope Numbers, Tetrahedral numbers and many more. The tetrahedral numbers use ... digit numbers and to see if it works the same way. The number in light blue is the first number in ...
... solutions to cubic equations and he was following the basics of addition, subtraction, division, and multiplication to compose a system that could be used with complex numbers. Although complex numbers was a significant invention in mathematics, this idea wasnt truly ...