Koosholts

Your signature is kinda freaky. What is it?

Yello. How are you?

That's hilarious.

Anonymous on arguing with Christians:

"It's like playing chess with a pigeon; no matter how good I am at chess, the pigeon is just going to knock over the pieces, crap on the board, and strut around like it's victorious."

My favorite part of the Bible is when God gives people free will and then kills them all with a flood for not acting the way he wanted.

I have another book suggestion for you. It’s called “This Will Make You Smarter: New Scientific Concepts to Improve Your Thinking”. The title is kind of corny, but it’s a really good book. It’s a collection of short essays by over 150 of the world’s top scientists in the fields of neuroscience, psychology, biology, engineering, physics and so on. There are also several essays written by respected scientific journalists and philosophers. The essays are about (from the point of view from their respective fields) why science is important, how it can help humanity be better human beings, how it strengthens our understanding of how the world and universe works, and how we should find meaning and purpose in life through reality and not the supernatural. It’s kind of a philosophy book written by scientists. It’s very interesting. It’s brand new too; it was published this year.

BARNES & NOBLE | This Will Make You Smarter: New Scientific Concepts to Improve Your Thinking by John Brockman, HarperCollins Publishers | NOOK Book (eBook), Paperback, Hardcover

I understand. Cases such as this in which the solutions are so similar can definitely be irksome. But if you think about it, it's supposed to be that way. Essentially, when the x's are all combined (either as 51x or -49x), there are no problems, but when they're separated (as in the preceding steps of the problem) there's a problem because one x is in the absolute value and the other isn't; this doesn't pose a problem to the positive solution because with the absolute value it remains positive, but the negative solution is altered in the absolute value while it remains the same outside of it, causing a negative number, and therefore an inequality, to be produced. I understand your thought process, but in this case it was only a matter of positive and negative.

I love math too, and you're welcome!

lol, we've all been guilty of that from time to time

No problem.

lol, you're not an idiot. Math is hard. Just ask your professor, I'm sure he/she can clear things up for you.

No, because the x = -1/7 solution should ultimately agree with the original equation. It's a false solution because -10 does not equal 10. You don't have to change 10 to its negative.

You're not supposed to change it to a -10. The negative answer is supposed to equate to the original equation based on the simplification of it, but it doesn't; that's what makes it the extraneous solution. If you were to make it -10, you would also have to get rid of the absolute value, in which case the solution still produces 10 =/= -10.

x = -1/7 is the extreneous solution. I can explain why if you want.

Sure, lay it on me.

|x - 7| / 5x = 10
|x - 7| = 50x
x = ±50x + 7
-49x = 7 OR 51x = 7
x = -1/7 OR x = 7/51

Logically, you should be able to substitute both answers in the original equation. When you substitute 7/51 into the equation it works out fine. However, when you substitute -1/7, it doesn't. This is because taking the absolute value of the numerator makes it positive, while the denominator remains negative; therefore, the quantity produced is not 10, but -10:

|-1/7 - 7| / 5(-1/7) = 10
|-7.14| / -5/7 = 10
7.14 / -0.714 = 10
-10 =/= 10

-1/7 is the extraneous solution.

Michio isn't religious at all, but he does like the idea of a Spinozan god/mechanism. The way he sees it, the laws of physics must get their nature from some entity (intelligent or not). He doesn't claim to know the nature of such a "thing" but assumes it must be kind of first cause that somehow gives nature its "nature". He often calls it the "God of Order". So yeah, in a sense he's kind of deistic, but a deist that doesn't claim such a "thing" to be intelligent; more of a natural mechanism by which things happen. Textbook deists believe in the supernatural, while Michio doesn't.

As for extreneous solutions, I'll let my friend Wikipedia explain it to you

Extraneous and missing solutions - Wikipedia, the free encyclopedia