- published: 22 Nov 2007
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In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.
The classic fallacious proof that 1 = 2. Written by John Gaspar. Produced by John Gaspar and Robert Kaplan. Class project for Multimedia Class of Ramapo College MSET program. Fall 2007.
A fallacious proof that 1=2. Lecture and script by John Gaspar. Explanation by Guy Reynolds. Produced by John Gaspar and Robert Kaplan. Class project for Multimedia Class of Ramapo College MSET program. Fall 2007.
This video is the first in a six-part series on the Gambler’s Fallacy. In this video I present the reasoning that leads to the Gambler’s Fallacy.
Mathematical fallacy In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. =======Image-Copyright-Info======== License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0) LicenseLink: http://creativecommons.org/licenses/by-sa/4.0 Author-Info: Turms Image Source: https://en.wikipedia.org/wiki/File:Fallacy_of_the_isosceles_triangle2.svg =======Image-Copyright-Info======== -Video is targeted to blind users Attri...
Here is the mistake: When I take the square roots of both sides, I get plus or minus terms. But in the video, I only take the plus terms of both sides. But if I take plus term of a side and minus term of a side, it will match. So the plus minus terms confuses you, you don't know what do you take. Do you take plus terms of both sides? Or do you take plus term of a side and minus term of a side? So the mistake is that I don't write "plus or minus" after taking the square roots of both sides. I just take the positive terms. For that, I get 2 =3. But if I take the positive term of a side and the negative term of the other side, I'll get 5 = 5 or -5 = -5 that is true.
How to prove if an argument is valid or a fallacy. For more free math videos, visit: http://www.professorserna.com
Arithmetical fallacies are represented by problems when put forth leading to obvious impossible results. For instance, proving 1=2 is a mathematical fallacy.
Math is invisible. Unlike physics, chemistry, and biology we can't see it, smell it, or even directly observe it in the universe. And so that has made a lot of really smart people ask, does it actually even EXIST?!?! Similar to the tree falling in the forest, there are people who believe that if no person existed to count, math wouldn't be around . .at ALL!!!! But is this true? Do we live in a mathless universe? Or if math is a real entity that exists, are there formulas and mathematical concepts out there in the universe that are undiscovered? Or is it all fiction? Whew!! So many questions, so many theories... watch the episode and let us know what you think! All Time 10 Videos: http://www.youtube.com/watch?v=UFydagCS9fg Veritasium - http://www.youtube.com/1veritasium (http://www.yo...
The power of angels
You left at my door
I wrapped it up
In tinfoil
And hastened away
Towards hills
Begging for someone
to give me a sign
But my heart wrapped in silver
Could cry any louder
Hello, the silver hearts
That you cannot remark
Go on, go on
You shall never know
You shall ever be