TED-Ed
TED-Ed: The paradox at the heart of mathematics: Gödel's Incompleteness Theorem | Marcus du Sautoy
Consider the following sentence: "This statement is false." Is that true? If so, that would make the statement false. But if it's false, then the statement is true. This sentence creates an unsolvable paradox; if it's not true and it's...
Other
Is All About Math: Mathematical Induction I
This podcast will give students an introduction and an example of the working of mathematical proof by induction. The presentation includes only two steps, which are explained thoroughly, and one example which students will understand....
Other
Is All About Math: Mathematical Induction Ii
This podcast expands upon the previous podcast, Mathematical Induction I, by introducing the case in which a proof is only meant to be valid for a certain set of numbers (ie, the proof may fail until the variable is higher than a certain...
Other
Is All About Math: Mathematical Induction Iii
In this podcast, which follows from Mathematical Induction Parts I and II, the narrator shows how to expand induction into the Principle of Strong Induction (used for more hard-to-prove theorems). The narrator runs through a few...
Khan Academy
Khan Academy: Vi Hart: 9.999 Reasons That .999 = 1
Video exploring number theory concepts such as real, hyperreal, and surreal numbers, and infinity. [10:01]
