{"id":1870,"date":"2009-01-22T09:10:39","date_gmt":"2009-01-22T01:10:39","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=1870"},"modified":"2014-06-13T16:12:52","modified_gmt":"2014-06-13T08:12:52","slug":"what-is-00-equal-to","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/what-is-00-equal-to-1870","title":{"rendered":"What is 0^0 equal to?"},"content":{"rendered":"<p>In the introduction to <a href=\"https:\/\/www.intmath.com\/exponents-radicals\/1-integral-exponent-laws.php\">Laws of Integral Exponents<\/a>, I mention the debate about the value of 0<sup>0<\/sup>. Is it zero or is it one?<\/p>\n<p>Why is it a problem? Look at the following 2 patterns:<\/p>\n<p>Multiply 0 as many times as you like, you get 0.<\/p>\n<p>0^3 = 0<br \/>\n0^2 = 0<br \/>\n0^1 = 0<br \/>\n0^0 = 0<\/p>\n<p>But then again, any number raised to the power 0 is 1:<\/p>\n<p>3^0 = 1<br \/>\n2^0 = 1<br \/>\n1^0 = 1<br \/>\n0^0 = 1<\/p>\n<p>That's why there is dispute about the value of 0^0. <\/p>\n<p>On the page linked to before, I wrote:<\/p>\n<blockquote>\n<p>It is most commonly regarded as having value 1<\/p>\n<\/blockquote>\n<p>An interesting conundrum. Sometimes our wonderful, (normally) consistent system of math breaks down. <\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/what-is-00-equal-to-1870#comments\" id=\"comms\">42 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Can 0^0 possibly have 2 values? This, like a few other math \"facts\", turns out to be controversial.<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/1870"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=1870"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/1870\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=1870"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=1870"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=1870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}