What's the largest number? What's a googol? How do we name large numbers? What is infinity?
What's the largest number?There is no largest number! Why? Well, 1,000,000,000 (1 billion) can't be the largest number because 1 billion + 1 is bigger - but that is true for any number you pick. You can choose any big number and I can make a bigger one just by adding 1 to it.
What's a googol?A googol is a 1 with a hundred zeroes behind it. We can write a googol using exponents by saying a googol is 10^100.
The biggest named number that we know is googolplex, ten to the googol power, or
How do we name large numbers?There's some disagreement in the English language about how to name large numbers. There are two systems, the American and the English:
Scientific American: Number Notation Thousand 1,000 10^3 Million 1,000,000 10^6 Billion 1,000,000,000 10^9 Trillion 1,000,000,000,000 10^12 Quadrillion 1,000,000,000,000,000 10^15 Quintillion 1,000,000,000,000,000,000 10^18 English: Thousand 1,000 10^3 Million 1,000,000 10^6 Thousand Million 1,000,000,000 10^9 Billion 1,000,000,000,000 10^12 Thousand Billion 1,000,000,000,000,000 10^15 Trillion 1,000,000,000,000,000,000 10^18And see: Decillion, Vigintillion, Trigintillion...
From the Dr. Math archives:
Adding Large Numbers on Calculators
Do Numbers Go On Forever?
Explaining Scientific Notation
Exponents in the Real World
Googolplex: Sheets of Paper
Large Number Division
Metric System Prefixes
Names of Big Numbers
Powers of 10
Prefix for 10^30 Bytes
Scientific Notation: Exponents
Teaching Large Number Concepts
From the Math Forum:
On the Web:
Googolplex - Frank Pilhofer
Graham's Number and Rapidly Growing Functions - Renfro
Mathematics: Numbers - Ft. Collins H.S.
Mathematics Archives: Numbers - UTK
Names for Large Numbers - Rowlett
Number Names - Fred Worth
Numbering Systems and Place Values - John Knoderer
RJN's More Digits of Irrational Numbers Page
What is infinity?
Infinity is not a number; it is the name for a concept. Most people have sort of an intuitive idea of what infinity is - it's a quantity that's bigger than any number. This is sort of correct, but it depends on the context in which you're using the concept of infinity (see below).
There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all. For the same reason, infinity is neither even nor odd.
The symbol for infinity looks like a number 8 lying on its
Now for the fun part! Even though infinity is not a number, it is possible for one infinite set to contain more things than another infinite set. Mathematicians divide infinite sets into two categories, countable and uncountable sets. In a countably infinite set you can 'number' the things you are counting. You can think of the set of natural numbers (numbers like 1,2,3,4,5,...) as countably infinite. The other type of infinity is uncountable, which means there are so many you can't 'number' them. An example of something that is uncountably infinite would be all the real numbers (including numbers like 2.34.. and the square root of 2, as well as all the integers and rational numbers). In fact, there are more real numbers between 0 and 1 than there are natural numbers (1,2,3,4,...) in the whole number line! See One infinity larger than another? for more information.
Lastly, please realize that the concept of infinity varies depending on what mathematical subject area you're talking about. If you're simply counting things up, then the picture looks something like this:
If you're talking about the number line, then the picture looks something like this:
If you're talking about the number of elements in a set, here's the picture:
If you're doing fancy geometry, you might have something like this (this is called Projective Geometry):
Finally, just for fun, here's another kind of geometry (Finite Projective Geometry) in which EVERY point can be called a point at infinity!2 Here the "lines" are the straight lines and the circle.
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