includes other24

Understanding the combinations formula, and using it to calculate the probabilities of various poker hands.

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Music:
"Lateralus" as performed by Sakis Strigas
Originally by Tool
https://www.youtube.com/watch?v=GN1Tf...
(ft. Scott Steiner)

"Rainbow in the Dark" as performed by Corey Taylor
Originally by Ronnie James Dio (requiescat in pace)

Horizontal Asymptotes for rational functions are usually presented as being "different" depending on how the degrees of the numerator and denominator compare. I'll show you why this is a pointless distinction.

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No textbooks were harmed in the making of this video.

3:26 Comment: Take the codomain of the function to be the extended real line. Then we have that z/0 = infinity (for positive z) and z/0 = -infinity (for negative z) as our asymptotes. Given the end behavior of such rational functions, viewing these as the horizontal asymptotes is appropriate.

Music:
Blue Wednesday - All That Jazz
https://soundcloud.com/bluewednesday

Two Steps from Hell - Heart of Courage
8-bit recreation by Floating Point
https://www.youtube.com/watch?v=VUmQK...

Asheru - Soul

The views expressed in this video in no way reflect the views of any university or organization with which I am affiliated.

Just like we can measure "how much" we have of an everyday object in different ways (mass, volume, length, etc) we can measure "how much set" we have in many different ways.

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(as well as previews, behind-the-scenes, and more content).

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blackpenredpen's video: https://www.youtube.com/watch?v=CuzEq...

Music by Sakis Strigas:

Undertow - Tool ( https://www.youtube.com/watch?v=Ip1d3...)
Fear Inoculum - Tool ( https://www.youtube.com/watch?v=Otw5k...)
Lateralus - Tool ( https://www.youtube.com/watch?v=GN1Tf...)

Why do we say that some things are "indeterminate" instead of "undefined"?

EXERCISE FOR THE VIEWER: Suppose we define a new number "x" such that 0x = 1. Show that this number violates the distribitive property.

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Music:
Blue Wednesday, All That Jazz
https://soundcloud.com/bluewednesday

"Fireside"
Instrumental by Homage
https://www.youtube.com/user/homage253

Outro:
Lateralus, as performed by Sakis Strigas
Originally by Tool
https://www.youtube.com/watch?v=GN1Tf...

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Music:
Lifeformed - Cider Time
https://www.youtube.com/watch?v=KXH5G...

A quick video working through some exponential equations with explanations.

For my students: These problems can be found in the exercises for Chapter 3.4.

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Music:
Jeff Kaale - Pillow Talk

Blue Wednesday - Cereal Killa, All That Jazz

Outro: Asheru - Soul

The views expressed in this video in no way reflect the views of any university or organization with which I am affiliated.