Educational Thread

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Re: Educational Thread

Post by TheDeceiverGod on 7/29/2010, 9:28 pm

It has come to my attention that math teachers in this country are horrible. This is apparently true no matter where you travel, or at least true everywhere I have traveled. They tell you what you need to know to pass their class, not what you should know to understand the material in their class. This irritates me greatly, so much in fact that I have decided to post here, the way Math should be taught. Or at least the way I believe it should be taught, starting with the basic rules of math, and moving on to addition.


Just for clarification:
+ is the symbol for addition. Addition is the simplest possible expression of mathematics, to add is to take one value and combine it with another value to gain a greater value. It is also used as the symbol for a positive value, a positive value is any value greater than zero. Though because positive is the natural state of a value, IE in the natural world it is more common to express the presence of something rather than the absence of something, positive values are often written without the positive value symbol.
- is the symbol for subtraction. Subtraction is the second level of mathematics, and means to take one value away from another value to gain a lesser value. The subtraction symbol is also used to represent a negative value, a negative value is the result of subtracting any value from zero. Negative values exist in opposition to positive values and this symbol is also sometimes called the opposite sign, as it may be used to represent the opposite value of something.
* is an asterisk, however for the purposes of this it will be serving as the symbol for multiplication. The traditional symbol for multiplication is the 'x' however since x is a popular letter to be used as a variable, due in large part to the dimensional axises being labeled x y and z, a dot or asterisk has come into common use.
Spoiler:
An asterisk a typographical symbol or glyph. It is so called because it resembles a conventional image of a star. Computer scientists and mathematicians often pronounce it as star (as, for example, in the A* search algorithm or C*-algebra). In English, an asterisk is usually five-pointed when typed and six-pointed when handwritten.

The asterisk is derived from the need of the printers of family trees in feudal times as a symbol to indicate date of birth. The original shape was seven-armed, each arm like a teardrop shooting from the center. For this reason, in some computer circles it is called a splat, perhaps due to the "squashed-bug" appearance of the asterisk on many early line printers. Many cultures have their own unique versions of the asterisk.
/ is a forward slash, however for the purposes of this it will be serving as the symbol for division. The traditional symbol for division does not appear on my keyboard, and due to the horizontal expression of fractions utilizing the a forward slash, and the fact that fractions are the simplified expression of partial numbers as a result of division, the forward slash will serve nicely as a replacement.
= is the symbol for an equality, this symbol represents the fact that whatever is on the left side of it is exactly equal to whatever is on the right side of it. This symbol is often used largely in theory or as part of a proof, where the mathematician is attempting to prove that the left is equal to the right.
^ is a caret, it will be serving as the symbol which will denote exponents, written as 1^2 to display 1 to the second power or one squared.
Spoiler:
The caret was originally used, and continues to be, in handwritten form as a proofreading mark to indicate where a punctuation mark, word, or phrase should be inserted in a document. The term comes from the Latin caret, "it lacks", from 'carēre', to lack; to be separated from; to be free from. The caret symbol is written below the line of text for a line-level punctuation mark such as a comma, or above for a higher character such as an apostrophe; the material to be inserted may be placed inside the caret, in the margin, or above the line.

Other symbols will likely be used but these will be the basics.


Deceiver's First Rule of Mathematics
All Math may be state in simple IF, Then sentences.


If one plus one equals two, then two minus one equals one. This is true only if we accept that one plus one equals two.

Deceiver's Second Rule of Mathematics
Excluding addition, all math may be proven by a lower level of math.


2*2=4 because 2+2=4

This is fact, no matter what level of math you are performing so long as it is not addition, than it may be proven by a lower level of math. Multiplication is proven by Addition, Subtraction is proven by Addition, Division is proven by Multiplaction, Exponents are proven by Multiplication, Negatives are proven by Subtraction. No matter how high up you go, there will always be a way to break something down into it's lower form. The reason why people don't simply express all math in it's lowest for is because it takes up an obscene amount of space. 2*9 is much simpler to write than 2+2+2+2+2+2+2+2+2 and when you get up even higher, it becomes far more expedient to use multiplication than to write out the addition, but despite this no matter how high up you get 2*9 will always mean the same thing as 2+2+2+2+2+2+2+2+2

Addition is the exception to this rule because no matter what you do it cannot be mathematically proven that 1+1=2, in all of mathematics there is no way to definitively prove this statement. We know it to be true simply because when you take one object and another object you have two objects, it is a law of reality, but not of Mathematics. Math has no way to prove that 1 and 1 make two, it simply has to take that as a given.

So if we know that 1+1=2 and that 1+1 is the same thing as 1*2 then we know that 1*2=2 because 1+1=2 and 1*2=1+1 which is the same as 2=2 which literally means that the value two is exactly equal to the value two.If you have two of something, then you have two of something.

Some people seem to get confused when mathematics is written with words in place of numbers. I can understand this it seems to me that most of this is because the people writing the questions are deliberately doing so in order to be vague annoying and difficult. This is one of the reasons I don't like people as a general thing.

In reality it is quiet simple to express a mathematical equation as a sentence. Take for example 2-1=1. If you have two things, and you take away one then you have one thing. Or if you really want to get complicated. You have two things, you take one thing away. You now have one less thing. How many things do you have?

You can write math a thousand different ways, but as long as you're talking about the same thing, than you're talking about the same thing.

Now then we know that Multiplication is just an elevated level of Addition right? That 2*4=2+2+2+2 which is the same as 1+1+1+1+1+1+1+1 because 1+1=2 2+2=4 4+4=8 1*8=8 2*4=8 and 8=1+1+1+1+1+1+1+1 because all of these things are talking about the same thing, they are all equal to each other. It doesn't matter how you write it, if it is equal to 8 then anything that also equals 8 is equal to it.

Well Division is really just lesser version of Multiplication. 8/4=2 because 2=1+1 and 8=1+1+1+1+1+1+1+1 and when you're saying 8/4 what you're saying is (1+1)+(1+1)+(1+1)+(1+1). If you have 8 and you want to break it up into four equal groups, then the only amount you can place into the groups is two. Two is the only value that will work in the entire universe, because only 2*4=8. Certainly there are other things which equal eight, but two is the only value in existence which when taken in groups of four will equal eight. 4 groups of 2 equals 8 total, 8 taken in 4 groups equals 2 for each group. If there are four equal groups, and there are eight items total, then there can only be two items in each group.

You may divide 8 into any number of groups you desire, but only specific numbers, will work to give whole numbers in each group and for each group to be exactly equal to the others. For example if you take 8/2, you will be able to get four equal groups of 2, this is because 4*2=8 because 8=1+1+1+1+1+1+1+1 4*2= (1+1+1+1)+(1+1+1+1) and 8/2=(1+1+1+1)+(1+1+1+1). If you have two groups of four, then you have eight objects total. The only thing that changes is the question. 4*2 asks how many objects are in two groups if there are four objects in each group, and 8/2 asks how many groups of two are there if there are eight objects total.

Division is the father of fractions. A fraction occurs when any number is divided by a number greater than it. For example 1 divided by 2 is a fraction. 1/2 is one half. If you have one object then the only way to make it fit into two equal groups is to divide it in half. This can be written as 0.5 or simply 1/2. Despite being written differently these two things are equal. 0.5 is five tenths, five equal parts each of which are one tenth of one whole object. 0.5=(0.1)+(0.1)+(0.1)+(0.1)+(0.1)=(1/10)+(1/10)+(1/10)+(1/10)+(1/10)=5/10=1/2 0.5=1/2

Again things are left in fractional form primarily due to convince, it is far easier to write 1/2 than it is to write (0.1)+(0.1)+(0.1)+(0.1)+(0.1)

0.1 is a decimal, decimals exist solely because it is sometimes necessary to write out the numeric value of a non-whole number, and just as 10 is ten times 1 1 is ten times 0.1 values of ten keep things simple and if Americans were sane they'd use them to measure things just like the rest of the world but they're not so they don't.

This is simply how we write numbers, the important thing is that 0.1 is exactly equal to 1/10 and that one divided by ten is exactly equal to one tenth. All these things are the same numbers, it doesn't matter how or where they appear they are the same numbers.

Moving right along exponents are the next level of Multiplication, 2*2*2=2^3 Two multiplied by itself three times. The exponent represents the number of times the base is multiplied by itself, the base represents the number which is multiplied by itself. There are various rules for dealing with numbers with exponents most of which make perfect sense if you simply understand that an exponent is nothing more than a simple way to write a number being multiplied by itself. For example if you have 2^6 * 2^4, instead of having to work out two times two times two times two, you can simply write 2^10. Why is this? Well 2^6=2*2*2*2*2*2 and 2^4=2*2*2*2 so 2^6 * 2^4=(2*2*2*2*2*2) * (2*2*2*2) all you're doing is multiplying 2 times itself ten times, so why not write it out as such? Thus if you have a number with an exponent, and then you have the same number with an exponent, you can simply add the exponents.

But this only works when you have the same base number. If you have 2^3 * 3^2 you cannot add the exponents together because you do not have 2*2*2 * 2*2 you have 2*2*2 * 3*3, and 3*3 is not equal to 2*2. Nor is it equal to 2*2*2 or 15,000*33*12. If you do not have the same base number, then you cannot add the exponents. Doing that is wrong and people like me will think you are stupid if you try to do that, because 2^3 * 3^2 is not the same thing as 2^5, you can do the math and find out.

That is the thing about math, you can do anything you like to something as long as it doesn't change anything.

Next Time on Learning Time with The Deceiver God Fractions, like numbers, only more complicated.
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Le Math

Post by TheDeceiverGod on 3/29/2012, 5:47 am

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Re: Educational Thread

Post by TheDeceiverGod on 4/2/2012, 3:31 pm

Thought this was neat and I'm aware there's a good number of aspiring artists on the forum. Plus we're thinking of starting up the Web Comic effort again and this just seemed like nail on the head reference.
Spoiler:


More where that came from.
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Re: Educational Thread

Post by archiesangel on 4/2/2012, 6:13 pm

Just watched the math video.. -mind blown-
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Re: Educational Thread

Post by TheDeceiverGod on 5/14/2012, 4:11 pm

Another video here. This one a little more philosophically inclined.

The guy starts talking about atheism and such, but I think it's really a better video to describe Nihilism-which is often misunderstood as, basically Owl Man from Crisis on Two Earths, but like everything has so many grey shades mixed in.

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Re: Educational Thread

Post by TheDeceiverGod on 8/23/2012, 10:19 pm

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Re: Educational Thread

Post by archiesangel on 8/27/2012, 4:45 pm

Very interesting...
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Re: Educational Thread

Post by TheDeceiverGod on 9/11/2012, 8:46 am

Learn about Andrew Jackson from Cracked.com
Trust me, you'll be glad you did.
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Re: Educational Thread

Post by Vandal on 9/11/2012, 11:52 am

I actually learned all that stuff from my history class. He seems a lot crazier in retrospect. That and maybe the drawings of him and his crazy eyes.

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Re: Educational Thread

Post by TheDeceiverGod on 9/11/2012, 12:45 pm

I just liked that they had to bait his own party with whiskey in order to get them out of the white house; and you have to love anyone who beats their own would-be assassin nearly to death.

I'd take it pretty personal if someone tried to kill me.
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Re: Educational Thread

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