{"id":1625,"date":"2015-12-08T14:36:29","date_gmt":"2015-12-08T20:36:29","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=1625"},"modified":"2015-12-08T14:36:29","modified_gmt":"2015-12-08T20:36:29","slug":"blogging-counterexamples","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2015\/12\/08\/blogging-counterexamples\/","title":{"rendered":"Blogging Counterexamples"},"content":{"rendered":"

I can\u2019t believe someone has been blogging about counterexamples<\/span><\/a> since July of last year\u00a0and I just found out! Luckily, the Aperiodical Advent Calendar<\/span><\/a> alerted me to it yesterday<\/span><\/a>, and now Math Counterexamples<\/span><\/a> is the newest addition to my blog feed.<\/span><\/p>\n

\"The<\/a>

The Smith-Volterra, or “fat” Cantor set, a great counterexample in topology. Image: Inductiveload, via Wikimedia Commons.<\/p><\/div>\n

Counterexamples have been on my mind a lot lately. This spring, inspired by a post I wrote about the \u03c0-Base<\/span><\/a>, an online analogue of Counterexamples in Topology<\/i>, I started writing about some of my favorite\u00a0spaces at my Scientific American<\/em> blog Roots of Unity<\/span><\/a>. Many of these spaces are counterexamples: connected but not path connected<\/span><\/a>, nowhere dense but having positive measure<\/span><\/a>, contractible but in no obvious way<\/span><\/a>. While my posts tend to be focused on geometry and topology, Jean-Pierre Merx, who writes Math Counterexamples, is an equal-opportunity counterexample-ist. His posts cover topics in\u00a0algebra<\/a> and analysis<\/a>\u00a0as well as\u00a0topology<\/a>.<\/span><\/p>\n

Like Tai-Danae Bradley\u2019s blog Math3ma<\/span><\/a>, which I wrote about a couple months ago<\/span><\/a>, I imagine Math Counterexamples would be a great resource for undergraduate or graduate students in math. (Their professors should probably pay attention, too: these are great resources to share with your students, but you may also want to make sure the questions you give aren\u2019t immediately google-able!)<\/p>\n

I\u2019m especially partial to the analysis counterexamples right now because they’re useful but I often have trouble cooking them up on my own. A recent post that caught my eye is about a function from R2<\/sup> to R with a local minimum at (0,0) on all lines through the origin<\/span><\/a> but which doesn’t have\u00a0a local minimum there when considered as a function of two variables. Weird, huh? If you go poking around the archives, I’m sure you’ll find some fun factoids too.<\/span><\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

I can\u2019t believe someone has been blogging about counterexamples since July of last year\u00a0and I just found out! Luckily, the Aperiodical Advent Calendar alerted me to it yesterday, and now Math Counterexamples is the newest addition to my blog feed. … Continue reading →<\/span><\/a><\/p>\n

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