Here we look at "quotient languages" and show an advanced topic in theory of computation - that we can show a DFA exists without knowing how to produce it. Moreover, we show that regular languages are closed under quotient, but also closed under quotient with any language at all! <br /><br />Easy Theory Website: <a href="https://www.easytheory.org" target="_blank" rel="nofollow">https://www.easytheory.org</a><br />Become a member: <a href="https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join" target="_blank" rel="nofollow">https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join</a><br />Donation (appears on streams): <a href="https://streamlabs.com/easytheory1/tip" target="_blank" rel="nofollow">https://streamlabs.com/easytheory1/tip</a><br />Paypal: <a href="https://paypal.me/easytheory" target="_blank" rel="nofollow">https://paypal.me/easytheory</a><br />Patreon: <a href="https://www.patreon.com/easytheory" target="_blank" rel="nofollow">https://www.patreon.com/easytheory</a><br />Discord: <a href="https://discord.gg/SD4U3hs" target="_blank" rel="nofollow">https://discord.gg/SD4U3hs</a><br /><br />#easytheory #gate #theory<br /><br />Youtube Live Streaming (Sundays) - subscribe for when these occur.<br /><br />Social Media:<br />Facebook Page: <a href="https://www.facebook.com/easytheory/" target="_blank" rel="nofollow">https://www.facebook.com/easytheory/</a><br />Facebook group: <a href="https://www.facebook.com/groups/easytheory/" target="_blank" rel="nofollow">https://www.facebook.com/groups/easytheory/</a><br />Twitter: <a href="https://twitter.com/EasyTheory" target="_blank" rel="nofollow">https://twitter.com/EasyTheory</a><br /><br />Merch:<br />Language Hierarchy Apparel: <a href="https://teespring.com/language-hierarchy?pid=2&cid=2122" target="_blank" rel="nofollow">https://teespring.com/language-hierarchy?pid=2&cid=2122</a><br />Pumping Lemma Apparel: <a href="https://teespring.com/pumping-lemma-for-regular-lang" target="_blank" rel="nofollow">https://teespring.com/pumping-lemma-for-regular-lang</a><br /><br />If you like this content, please consider subscribing to my channel: <a href="https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1" target="_blank" rel="nofollow">https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1</a><br /><br />Gold Supporters: Micah Wood<br />Silver Supporters: Timmy Gy<br /><br />▶SEND ME THEORY QUESTIONS◀<br />[email protected]<br /><br />▶ABOUT ME◀<br />I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.<br />...<br /><a href="https://www.youtube.com/watch?v=PgUB_07N0eA" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=PgUB_07N0eA</a>