{"version":"https:\/\/jsonfeed.org\/version\/1","title":"mathspp.com feed","home_page_url":"https:\/\/mathspp.com\/blog\/tags\/rationals","feed_url":"https:\/\/mathspp.com\/blog\/tags\/rationals.json","description":"Stay up-to-date with the articles on mathematics and programming that get published to mathspp.com.","author":{"name":"Rodrigo Gir\u00e3o Serr\u00e3o"},"items":[{"title":"Twitter proof: irrational rationality","date_published":"2017-11-16T00:00:00+01:00","id":"https:\/\/mathspp.com\/blog\/irrational-rationality","url":"https:\/\/mathspp.com\/blog\/irrational-rationality","content_html":"<p>Let's prove that there are two irrational numbers, call them <span class=\"mathjax mathjax--inline\">\\(a\\)<\/span> and <span class=\"mathjax mathjax--inline\">\\(b\\)<\/span>, such that <span class=\"mathjax mathjax--inline\">\\(a^b\\)<\/span> is a rational number! And let's do it in a tweet.<\/p>\n\n<script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<p><img alt=\"the variable a raised to the power of b\" src=\"\/images\/c\/0\/1\/8\/9\/c01897bba8131bf7b98121f7fb8f67c3b759995a-atotheb.webp\"><\/p>\n<blockquote class=\"twitter-tweet\">\n<p lang=\"en\" dir=\"ltr\">Twitter proof:<br>Let a=b=\u221a2. If a^b is rational then there is nothing to be done. Assume a^b is irrational. Redefine a=\u221a2^\u221a2. Notice how a^b = (\u221a2^\u221a2)^\u221a2 = (\u221a2)^2 = 2 which is clearly rational. QED.<a href=\"https:\/\/t.co\/3sFinyzJwu\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"external-link no-image\">https:\/\/t.co\/3sFinyzJwu<\/a><\/p>\u2014 Mathspp (@mathsppblog) <a href=\"https:\/\/twitter.com\/mathsppblog\/status\/1286089355732365313?ref_src=twsrc%5Etfw\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" class=\"external-link no-image\">July 23, 2020<\/a>\n<\/blockquote>\n<p>Do you have an idea for a twitter proof? Let me know in the comments below!<\/p>","summary":"A really short proof that there are two irrational numbers whose power gives a rational number.","date_modified":"2025-07-23T16:49:02+02:00","tags":["arithmetic","rationals","mathematics"],"image":"\/user\/pages\/02.blog\/irrational-rationality\/atotheb.webp"}]}