Is there a mathematical notation for a very very big numer?

Question

I am not a mathematician but a need, for a document, a standard mathematical notation or symbology for:

a)A very very big known number, like a Google Plex
b)A ver very big unknown number, e.g. no yet determined but bigger

A Latex symbol or notation would be fine. In fact any help or link would be highly appreciated.

Answer 1

From your details I gather you mean a very big, BUT FINITE, number. (The 'sideways-eight' symbol for infinity is well-known ... but there are many orders of infinity [cardinal or ordinal infinities], and they all have their own symbols [e.g. using the hebrew letter Aleph], which I won't get into.)

There are many notations and symbols for very large-but-finite *known* numbers. I assume you know about exponents, exponential notation, and factorial notation.

I don't know of any symbol for a googol (1 raised the 100th power) or a googolplex (1 raised to the googol power).

Jonathan Bowers also extended this to name other large numbers (giggol, giggolplex, boogol, etc.). These are described in another nice page (see source #2) that also describes some of the following very-large-numbers.

There is also "Graham's number", which is much larger than a googolplex, and I believe is still the record-holder for the largest finite number used in a mathematical proof. It is too large to be written with exponential notation (including stacking exponents!) ... but can be expressed using Knuth's up-arrow (which I can't reproduce here on Yahoo ... but see source #3 below).

Also, besides Knuth's up-arrow, there is also Conway's chained arrow notation (see source #4).

But you should also check out Steinhaus–Moser notation (see source #5 below), including the very large "Moser's number." The notation uses a very interesting number-within-a-polygon symbology.

Many of these numbers are so unimaginatively huge, that they are more the product of playing with notation systems themselves, rather than the numbers having any useful purpose or meaning.

As far as symbols, note that Knuth (of the Knuth up-arrow notation) is also the developer of TeX, so these *notations* are generally supported in LaTeX. However, a notation is always a way of expressing large numbers in terms of smaller ones. So that is why these large numbers rarely have a specific symbol.

Answer 2

The ^ sign means "to the power of" or exponentation.

The first symbol you might use is exponential notation. For example, 1 x 10 ^ 100 is a googol. Numbers like that are always in the form of a x 10^b. 'a' is called the mantissa, and 'b' is called the exponent, also the "order of magnitude", because for big numbers, it gives an appropriate estimate.

For bigger numbers, you might consider the "Up Arrow" notation. That is an extension of the pattern: multiplication is repeated adding, and an exponent is repeated multiplying. A double arrow is repeated exponenting!

2 ^ ^ 3 = 2 ^ (2 ^ 2) = 2 ^ 4 = 16.
2 ^ ^ 4 = 2 ^ 2 ^ (2 ^ 2) = 2 ^ (2 ^ 4) = 2 ^ 16 = 65536

A triple arrow is repeated double exponenting!

2 ^ ^ ^ 3 = 2 ^^ (2 ^^ 2) = 2 ^ ^ 4 = 65536
2 ^ ^ ^ 4 = 2 ^^ 65536 = 2 ^ 2 ^ ... ^ 2 (repeated 65536 times!)

and so on. These numbers get big fast, which is why you need the notation!

Answer 3

First off, DON'T use the infinity (∞) symbol. ∞ is supposed to mean an infinite number, which is not a discrete value at all. If you're looking for a very large known or unknown value, ∞ means nothing to your problem because ∞ has no value.

For a very large known number, use scientific notation.
A googol, for example, is 1 × 10^100 (ten to the hundredth power). Computers and calculators these days use exponentiating notation, which is the same thing, except substituting E for the "10 to the power" bit. A googol would be 1E100.

As another example, Avogadro's number is another large known value.
In scientific notation: 6.022 × 10^23
In exponentiating notation: 6.002E23

For a very large unknown value, the common practice in analysis and operations research is to use M. The "Big M method" is used with inequalities to represent a number so large that it would overwhelm the other variables in an equation.

Answer 4

Hi. Raising a number to a power is probably the best, as already pointed out. An example would be "What is the highest number you can make using three 9s?". Not 999, not 9^99 (although that's a pretty big number). 9^9^9. This is an ENORMOUS number. A google is 10^100 and this is more than all the atomic particles in the known universe. A googleplex is 10^10^100, or 10 raised to the power of a google. But even this number is tiny compared to infinity.∞

Answer 5

→∞

Approaches infinity - the simbol is the tilted 8 with an arrow before it and pointing to it.

infinity

In general, infinity is the quality or state of endlessness or having no limits in terms of time, space, or other quantity. In mathematics, infinity is the conceptual expression of such a "numberless" number. It is often symbolized by the lemniscate (also known as the lemniscate of Bernoulli), which looks something like the numeral 8 written sideways (∞). This symbol for infinity was first used in the 1600s by the mathematician John Wallis.

Infinity
Instead of investigating what happens with a function as its argument approaches a real number, one can ask how a function behaves as its argument increases and remains larger than any real number, or as it decreases and remains less than any real number.
We will say that a quantity ``approaches positive infinity'' if it eventually exceeds and remains larger than any given number. We will say that a quantity ``approaches negative infinity'' if it eventually falls below and remains less than any given number.

Answer 6

There are several ways. Large numbers are written using exponentials or powers. When you start stacking powers you take powers to powers, which are incomprehensibly large. Even these become cumbersome, so the "up-arrow" was invented. This sybolism is used to represent the very largest numbers, far great than the number of subatomic particles that could be stuffed into the known universe.

Heady but neat stuff.

Answer 7

E = EXPONTATE

4.0E99
THIS MEANS 4 FOLLOWED BY 99 ZEROS
4.0E-99
THIS MEANS 4 PRECEEDED BY A DECIMAL POINT AND 99
ZEROS

EXAMPLES
4.0E5 = 400000
4.0E-5 = 0.000004

Answer 8

tan 90

Answer 9

take two circles and mash them together horizontally, that's the symbol for infinity
like OO but closer together

Answer 10

big ---- 1.0 e^{10}
Bigger ---- 9.9 e^{99}
Really Big ---- 6.6 e^{6^6}
Freaking Huge ---- \frac{1}{e^{-9^{9^9}}}

for a unknown number \mathcal{N} \aprox \infty