The Concept of Number

The concept of Number is a foundational element of mathematics. It describes ways to quantify, measure and label quantities, and it can be used in many different settings. For example, numbers can be used as symbols to represent decimals in a scientific formula or as words to describe percentages in a marketing report. A number can also be used to represent a rank or order in a system.

When it comes to writing about numbers, communication pros often struggle to know how much to spell out vs. how much to use numerals. This can be especially challenging because the rules around this subject are inconsistent and vary from style guide to style guide. However, with consistent and careful editing and proofreading, even a writer who hates math can write about numbers accurately and helpfully.

Generally, the word number is used with uncountable nouns, while the word quantity is usually used with countable nouns (such as trees or fish). The phrase amount of is often considered more formal than the phrase a lot of and can be followed by a positive or negative adjective such as huge, big, large, small, etc. Amount of can also be followed by a verb such as to make, to take, to get, or to give.

While the concept of Number is broad, there are a few basic elements that all numbers must possess in order to be considered a number. For example, a number must be part of a number system. A number system is a set of entities that can be combined by addition, subtraction, multiplication and division, producing answers that are also members of the set. This includes number systems with a rational base, algebraic integers, complex Number_i and ordinals.

It is also necessary for a number to be positive or at least non-negative. Negative numbers are also called irrational and are characterized by the fact that they cannot be written as the product of two integers. Positive numbers are also known as real numbers and can be represented by a circle with its endpoints connected by lines. Other types of real numbers include constructible and complex numbers.

Finally, a number must be able to represent an ordered set. The most common ordered sets are binary and decimal, but there are also p-adic numbers, algebraic integers, cardinals and ordinals.

If you follow these guidelines, you can safely use numerals for all numbers under ten and spell out all other numbers. Using consistency in your manuscripts is also important, and this can be done through consistent formatting choices. For example, if you choose to use numerals for all numbers over 10 and words for smaller numbers, be sure to stick with this throughout the entire manuscript. In addition, it is a good idea to check the guidelines of your target publication to see what their style is. Ultimately, the most important thing when writing about numbers is to be transparent and honest with your readers.