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Politics : PRESIDENT GEORGE W. BUSH -- Ignore unavailable to you. Want to Upgrade?

To: ManyMoose who wrote (326136)	12/5/2002 11:24:03 PM
From: J_F_Shepard	Read Replies (1) \| Respond to of 769670

"They're not mutually exclusive." Yes, they are..... A child may not understand why a gas expands when it is heated but even he can prove it does by warming a balloon over and over again...as he gains more scientific knowledge he will understand why. It's true that expert scientists or mathematicians are not expert in all fields just as MD's are not experts in all fields of medicine. But there are people who are experts and who have knowledgeable colleagues all over the world. In religion, religious leaders and even many lay people claim to understand, if they believe, how the universe was created, how life was created, who the first humans were, that a human was a god, etc etc.... And all without experimental proof or substantiated evidence....all just on faith. Miracles are claimed but can't be repeated..jAll miracles are unique....visions are seen but not by all. More religious education doesn't verify with experiment and understanding, it just reinforces the same old beliefs....these folks must be absolute geniuses.... You mentioned imaginary numbers....can you explain them? Do you need religion, ie a belief, to understand them? I don't think so.....here's the explanation in easy to understand terms: mathforum.org Ask Dr. Math: FAQ What is an imaginary number? What is i? Contrary to what some people might tell you, imaginary numbers are not numbers that only exist in the brains of weird people. Or maybe they are; all numbers in math are "imaginary" in the sense that you can't touch them or experience them directly. But this is not what people mean when they talk about imaginary numbers. Imaginary numbers are numbers that can be written as a real number times i. So what is a real number, and what is i? Well, the real numbers are all the positive numbers, negative numbers, and zero. These are numbers like 5 -2.9 -4/3 0 1.11211211111221312211131122211113213211... (bonus points if you can tell us what the next few digits are and why!) So the real numbers are the numbers that you probably already know: they're the ones on the number line. What is i? It's the square root of -1 (see footnote below). And it's NOT a real number. i was invented because people wanted to be able to take square roots of negative numbers, and you can't do that if you limit yourself to real numbers. So we can make an imaginary number by taking a real number like 5 and multiplying it by i. That gives us 5i. Some other imaginary numbers are 37.3i 1.11211211111221312211131122211113213211i Pi*i. Note that the square of any imaginary number (except 0) is a negative number. Complex numbers are numbers like 7 + .4i; they're a real number plus an imaginary number. Footnote: actually, there are TWO numbers that are the square root of -1, and those numbers are i and -i , just as there are two numbers that are the square root of 4, 2 and -2. Browse the Dr. Math archives to find answers written for a variety of levels. Here are five: Elementary / About Numbers: What is i? Middle / About Numbers: The Imaginary Number Advanced / Complex Numbers: What Are Imaginary Numbers? Advanced / Complex Numbers: What is the Square Root of i? Advanced / Complex Numbers: Graphing Complex and Imaginary Numbers And don't miss this commentary on the word "imaginary number": Imaginary Numbers, History and Commentary - Howard Engel <http://mathforum.org/dr.util/star.gif> .