{"id":4676,"date":"2013-06-07T00:01:17","date_gmt":"2013-06-07T07:01:17","guid":{"rendered":"http:\/\/www.wambooli.com\/blog\/?p=4676"},"modified":"2013-06-01T12:28:09","modified_gmt":"2013-06-01T19:28:09","slug":"numbers-numbers","status":"publish","type":"post","link":"https:\/\/www.wambooli.com\/blog\/?p=4676","title":{"rendered":"Numbers Numbers"},"content":{"rendered":"

A number is a number is a number, until you bump into a mathematician. At that point you can seriously question your sanity.
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\nComputers deal exclusively with binary numbers<\/em>. That means only ones and zeros. Thanks to deception I care not to explain, those 1s and 0s can represent two types of values: integers<\/em> and floating point<\/em> values.<\/p>\n

Integer.<\/strong> An integer<\/em> is essentially any value without a decimal part, also known as a whole number<\/em>. Integers can be positive or negative, such as 5 or -5. Two additional, annoying terms used to describe integers are signed<\/em> and unsigned<\/em>; a signed integer can be positive or negative, an unsigned integer is always positive.<\/p>\n

Floating point.<\/strong> Any value can be a floating point<\/em> number, although values with fractional parts are what this type of number is designed to store.<\/p>\n

The term precision<\/em> is often used when referring to a floating point value. That’s because computers are able to accurately display only so many digits of very tiny or very large values before the system goes nuts and starts making things up.<\/p>\n

I’m serious: A floating point value with 8 digits of precision means that any numbers after the 8th digit are just junk. Computer scientists have been able to successfully deal with precision so that rockets actually make it to the moon and big buildings don’t fall down.<\/p>\n

Beyond computer science, other ways to describe a number exist, each of which can be as confusing as a t-shirt with a third arm hole:<\/p>\n

Whole Numbers.<\/strong> Any number that’s not a fraction.<\/p>\n

Natural Numbers.<\/strong> Mathematicians aren’t certain about natural numbers. Think of the values as counting numbers. Some eggheads claim natural numbers start with 1 and go on up, just as a human would count.<\/p>\n

Nominal Numbers.<\/strong> This type of number is used for naming purposes. For example, if your home address is 1322 Pumpernickel Drive, the 1322 is a nominal number. It doesn’t mean that yours is the 1322nd house on the street.<\/p>\n

Now things start to get weird.<\/p>\n

Real Numbers.<\/strong> A real number is just about any number. It’s the equivalent of a floating point value for a computer. Real numbers measure things and can be expressed in a variety of ways. That begs the question of whether unreal numbers exist.<\/p>\n

Unreal Numbers.<\/strong> The unreal number is not a mathematical construct. Surreal numbers<\/em> exist, but that’s a topic for Einstein and Mr. Spock to debate. What is probably meant by unreal numbers is something along the line of a transcendental number<\/em> or an irrational number<\/em>.<\/p>\n

Trascendental Numbers.<\/strong> A transcendental number is a value that cannot be expressed using forms of algebra you haven’t used since the 10th Grade.<\/p>\n

Irrational Numbers.<\/strong> An irrational number is any value that cannot be expressed as a fraction, such as 3\/2 = 1.5. The value π is an irrational number, as are the famous values e<\/em> and √2.<\/p>\n

By the way, the value π is both irrational and trascendental. The √2, however, is only irrational because it can be expressed by using a polynomial equation.<\/p>\n

Aren’t you happy you’ve read this far?<\/p>\n

Finally, if irrational numbers exist, do rational numbers<\/em> exist? Of course!<\/p>\n

Rational Numbers.<\/strong> A rational number can be expressed as a fraction, which is the opposite of the irrational number. And even though the national debt is a rational number, the whole concept is irrational, so don’t let that information tidbit confuse your further.<\/p>\n","protected":false},"excerpt":{"rendered":"

A number is a number is a number, until you bump into a mathematician. At that point you can seriously question your sanity.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-4676","post","type-post","status-publish","format-standard","hentry","category-main"],"_links":{"self":[{"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4676","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4676"}],"version-history":[{"count":7,"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4676\/revisions"}],"predecessor-version":[{"id":4688,"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4676\/revisions\/4688"}],"wp:attachment":[{"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4676"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4676"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wambooli.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4676"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}