A number is an abstract entity used originally to describe quantity. At least, that was, until the invention of complex numbers and now this definition must be relaxed. Numbers surround us all the time whither as phone numbers for singles bars or the watch on your wrist. Most humans begin this mathematical experience at the age of four when they are taught the numbers ranging from 1 to 10. However when you reach the age of adult you are hit with the idea that 1 to 10 does not suffice in most calculations. In fact there are a great many different types of numbers:
Natural Numbers Natural numbers are the digits to which we have already been accustomed and then some i.e. the range 1 to infinity.
Whole Numbers Whole numbers are not actually that different from natural numbers except that the range now includes the number 0. Why mathematicians choose to make an entire new name for this range is currently beyond the thinking of any mortal and thus has been deemed an act of the alien contingent that found themselves stranded on earth in the late 1st century. (Full details on the workings of this mysterious group have never been found due to their consumption by the Loch Ness monster.)
IntegersIntegers are whole numbers but they include all the positive and negative versions of themselves, i.e. integers range from negative infinity to positive infinity. (-∞ to +∞)
Rational and Irrational Numbers Rational and Irrational numbers are neither responsible nor illogical (though many would contest to the latter). These numbers discern whither a number can be expressed as a fraction or not. Rational numbers CAN be expressed as a fraction and therefore include all values greater than 0 and less than 1. .220138028902 and 21312.43793 are rational, along with the natural number 2,137,120,981,470,498.
Irrational numbers CANNOT be expressed as a fraction and therefore include a number of ‘roots’ of numbers which we shall return to later.
Trans-infinite Numbers Trans-infinite numbers are numbers that are greater than infinity. (No, I am not crazy. Just strech your imagination.) These numbers include the numbers made by Georg Cantor, א0 through א∞. These numbers are called aelph-null and aelph-infinity. (Please note that only aelph-null through aelph-two have practical use) and the numbers א0 (beth-null) through א∞ (beth-infinity) used in the Continuum Hypothesis, plus others.
Imaginary Numbers Imaginary numbers are numbers which do not in fact exist (as their title would imply). Mathematicians saw fit to create another group of numbers after discovering that there just weren’t enough to go round. And so the ‘root’ of negative 1 was given a very imaginative symbol of ‘i’ which is currently used in a great many of usefully useless equations and diagrams.
Mathbooks as Direction Maps -- Warning!
With the collaboration of the last two groups it is easy to end up with ‘numbers’ which are equal to numbers which read (i60)+√3, or I (interstate) sixty three plus ‘route’ three, it could be possible to, but do not to use the latest maths textbook as a means of direction when travelling around America, though the irrelevant question may somehow by the miraculous powers of the people that wrote it be related to the train tracks that run though Washington; it will not, I repeat not, get you to New York City in a record 15 seconds.
π and e There are two further important companions of the mathematician. One of them is geek letter 'π', pronounced pie, but spelt pi. This special number (3.141592…) has no discernable pattern to its decimals and in fact is completely random in structure. Humans have created a so called super-computer to spend the rest of its inanimate life working out this number to as many decimal places as possible and try to work out a pattern, thus far it has been calculated to over 10 million decimal places and still they search for a connection. This number is used to equate the radius of a circle to its circumference and ultimately its area. This number is often used by children studying maths however for the most part it only succeeds in making them hungry and causing them to dribble saliva from their open mouths on to the afore mentioned calculations, making the entire task irrelevant and sloppy. Another number which mathematicians claim is important is the number "e" though it may in fact look like a letter it represents the number and is also known as the natural log (not part of a tree). A number which stays the same if you integrate (boring) it or differentiate (complicated and more boring) it stays the same. Imagine that, after all the manipulating and changing, the mathematicians decide that a number which stays the same is important to them. There are many other numbers too.
Therefore it can be concluded that numbers are extremely complicated things but not half as complicated as the mathematicians that make them.
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