Gar1eth

I'm trying to help @AdamSmith in his quest to spread enlightenment to our Forum Brethren. And sadly-sigh-this is the thanks we get. Gman

FOIL ( a + b) times ( a - b) First a X a = a ^ 2 Outer a X -b = - ab Inner b X a = a X b = + ab Last b X - b = - b ^ 2 So a ^ 2 + (-ab) + (ab) - b ^ 2 = a ^ 2 - b ^2 If b = a you get the equivalent expression @AdamSmith used. @quoththeraven you are correct that the original expression is equal to zero. That's part of the trick in these proofs. Using letters instead of actual numbers, people often lose sight of that. Gman

No it's right. It's called 'factoring the difference of (perfect) squares. See the video below. According to what my 10 th grade geometry teacher said (and maybe my 1st year algebra teacher the year before), all these proofs rely on dividing by zero at some point. It's usually cleverly 'disguised' so you can't always pick it out. It's also one reason why math teachers don't actually like you to say that you are 'cancelling' out factors on both sides of the equation. What you are actually doing is dividing by the factor in question. And if you know the factor is = to zero, you know you can't actually do it. Here's the reason line 2 is correct @quoththeraven. If you don't like this video-you can go from the other direction and use the FOIL (First-Outer-Inner-Last) Method to multiply (X + Y) times (X - Y) to see that it gives you (X ^2 - Y ^ 2) but you can substitute X for Y and it gives you the example above. Gman

It took me a second. But I remembered something my 10th grade geometry teacher pointed out to my class (40 years ago now) when she performed a similar proof. (X - X) is equal to zero. You can't divide by zero and remain in the Real Number 'Realm'. Therefore @AdamSmith your proof is sadly invalid. Gman PS Now if I could only remember where I put my glasses 10 minutes ago.

If you 'hit it', might you not drive it in deeper? Gman

See my reply above this comment. Gman

How silly. George shouldn't have used the term 'average' he should have actually said, "Think about how stupid the MEDIAN person is... Median- mathematics : the middle value in a series where half of the set are above the value and half are below. Gman

http://i76.photobucket.com/albums/j12/itsallos/F2B904B5-631B-4080-9CA5-BFAB8F708799_zps2nojda24.jpg Gman

Nobody except another sufferer knows the nights of agony I've endured. And now I continually have phantom pains!! The Onion Report: Male Hair Loss 7 Times More Painful Than Childbirth http://i.onionstatic.com/onion/1587/2/16x9/1200.jpg NEWS IN BRIEF August 23, 2011 VOL 47 ISSUE 34 · Science & Technology LOS ANGELES—According to a study released Wednesday by the California Pain Medicine Center, subjects suffering from male- pattern baldness were found to experience a level of physical pain at least seven times more intense than that experienced by women during childbirth. "Clinical studies show that as hair gradually separates from the scalp, men experience intensifying waves of all-consuming pain equivalent to having their insides ripped out through the thousands of tiny follicles on their head," said Vincent Kwan, who led the all-male research team that carried out the study. "While strong uterine contractions and tearing of the vaginal walls undoubtedly cause a degree of discomfort among women in labor, balding men would give anything to experience those sensations instead of lying awake and suffering all night as their hair thins." Kwan stated that men's remarkable ability to endure years of excruciating agony without the aid of epidurals or other powerful analgesics was a testament to the sex's unrivaled tolerance for pain. Gman

For all you cooks out there-- Isn't technology wonderful? Gman

Ha Haaa Ha!! http://d.justpo.st/media/images/2015/06/21/im-calling-from-my-new-android-smartphone-yes-it-even-includes-unlimited-data-star-trek-the-next-generation-1434896517.jpg Gman

Is that supposed to be Machiavelli? Gman

I would think a tree-hugger driving a hybrid shows congruence rather than a dichotomy. If a tree-hugger isn't walking, riding a bike or driving a totally electric car, what better car to drive than a hybrid which is supposed to be more environmentally friendly than a gas guzzler? Gman

I'm confused. Does her getting to drive in the carpool lane help you in someway? Gman

Yes-Love them!!! Gman

It's good @Truereview. Of course I'd like it better if it were 'whirled peas'. Gman

Nope-that's your 2nd strike with a full count pending. I consider that an especially egregious stereotype which I dislike intensely. Plus I hate shrimp. Gman

A bit except I don't like looking at a--holes. Gman

Sorry Adam-can't give a 'like' to this one. Gman

Gman

A bit old. But still a goody. Gman

Gman

I'm repeating this post from the Friday Funnies. It's probably more appropriate here. http://i76.photobucket.com/albums/j12/itsallos/Mobile%20Uploads/2016-02/D3618331-D19D-4D5F-BFD9-BF065C2A84AF.png_zpsqsv0n20i.jpeg Gman

Set phasers to char!!!!! Gman

You have pictures of Smokey The Bear and you? Did you and @geminibear have a Bearfest in the wilderness? http://img.izismile.com/img/img3/20101028/video/11_bears.jpg Gman