Proof: Product of Absolute Values is the Absolute Value of the Product

The product of the absolute values of two real numbers is equal to the absolute value of the product of the numbers. That is, for all a and b in R, |a|*|b| = |a*b|. We prove this basic result about the absolute value function in today's lesson using three cases.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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[WrathofMath]

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[phi]

Another way to do so just using the laws of exponents: since |x|=√x² ; |a||b| = √a²√b² = √a²b² = √(ab)² = |ab|. The method you demonstrated is still more intuitive!

[valeriereid]

Thank you for these excellent videos in real analysis. Do you have any videos for complex series and sequences?

[lynne]

Thank you so much!!! This was the exact problem for my homework! Thank you for explaining it :D

[Bermatematika]

Here is another way. When a or b is zero the result is obvious. Assume a and b are nonzero. First prove that |x|^2 = x^2. By using this |a| |b| and |ab| are positive solutions to x^2 = a^2b^2. Hence they must be equal since the solution is one positive and the other one is negative.

[joehudson]

I do video lectures on tik Tok. I also implement the same techniques up above.

[arthurlukhozi]

Hi, which textbook do you use to prepare for your lessons?

[dutonic]

Hello! Does this real analysis playlist follow a textbook? Or do you just pick relevant topics and write your own stuff

[_jaishreerana]

Thank you sir, this video helped me alot.

[evabeyza]

it is a bit confusing because any number in absolute value cannot be equal to the negative of this number. labl = -ab is wrong. We should write labl=l-abl=ab

[Ahadi]

Please explain Cage- amalgamation graph, how we cane find it?
thanks

[cosmic_atanu]

can you please make about number system construction

[bat_man]

Thank you teacher, really helpful series 😊

[KamelHamidu]

Thank you so much, I have spend a lot of time trying to understand this but it didn't workout, thanks to your video I have understood it.

[LizT-qftl]

Does this change at all if a and b are complex numbers? Does the addition of real numbers to imaginary numbers affect the multiplication?

[nic]

Quick Question: Is there a reason why we omit the case where a>=0 and b<0?

[mike_the_tutor]

I haven't found any videos on YouTube covering the drinker paradox or the fallacious proof by induction that all billiard balls have the same color. I know that Mu Prime Math has done a geometric proof on why the cross product distributes over vector addition but I would love another video with some of the steps broken down a bit more. Just some ideas for you, take 'em or leave 'em. Thanks for all of your excellent proof videos.

[ايمانعلي-ظت]

Hello, Hello I can help me I am looking for a different and different profiles on the collection of groups, for example, books or sources or files I need to complete my reply please reply☺

[kaglet]

Short, sweet and straight to the point. Thank you :). If anyone knows, what's the music at the end?