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Algebra Is An Introduction To The First Most Naturally Effective Tools In Mathematical Operations
In our article about the early operation tool on arithmetic systems, we point out several kinds of formats, that can be addressed by acceptable geometrical identity called symbols in a format of sign, numbers, and alphabetical. For example: “eighty-four” is one kind of format, that we can be called as numbers, or some people called as even numbers. For us to solving more variants on the universe game called operational system, which is like a number eighty-four that taken from acceptable geometrical identity symbols in a form of sign like “8” and “4”, which we write them together as “84”. Now we want to discuss one general major in the sub-branch of mathematics that will be taken with more geometrical symbols, like the alphabet of a, b, c, and many more, with no especially focusing on specific numbers but into all kinds of groups of numbers. this type of mathematics gets addressed now on as algebra.
We could explain the differences between the arithmetic operation tool and algebra by simple example like if we take some random number and let's say this is our original number, and this number is 4. We multiply the number of 4 by 5, then we can write as 4 * 5 = 20, we are adding it by 4, then we write it 20 + 4 = 24, the result we multiply it by 2, which is 24 * 2 = 48, then we subtract it by 8, which is 48 – 8 = 40, and let say for the last at this moment, we divide it by the original number itself, which our original number, in this case, is 4, then this will give us 40 / 4 = 10. Therefore, this result of arithmetic operational tools is 10 as we see it. During our process to get the final value of 10, we are using the arithmetic operation tool in which during the process we all need some specific numbers.
Meanwhile, if we think about those numbers, then let us define each of those numbers by recognizable geometrical identity in the format of alphabetical as an “x” and let us do the arithmetic operational tool that similarly as we have in the previous paragraph. If we multiply “x” by 5 in terms like x * 5, then we will have 5x, we are adding it by 4, then we will have 5x + 4, the result we multiply it by 2, which is (5x+4)*2 and that gives us 10 x + 8, then we subtract it by 8, in which we will have 10 x + 8 – 8 = 10x, and lastly we will divide it by our original value, which is, in this case, is “x”, therefore we will have 10x / x = 10. Voila, we have a final result of 10. In this case, we have using an algebra method instead of arithmetic operational tools, this is because the value of the “x” symbol in this scenario can get exchange by any kind of value. We can change it to a value of 2, or 3, or 15, and whatever numbers value that we pick, then we will always be ended with a final result of 10.
If we have general numbers, that been addressed symbolically by an alphabet like “x” multiplied by some numbers like “5” or by some other alphabet like “y”, then we could not be using the symbol of multiplication, but to addressing that multiplication by writing those symbols closer each other. For the example: x * y = xy, or 5 * x = 5x, or 5 * x * y = 5xy. On the other hand, if we don’t use the alphabetical symbols then we could not write it like that, an example 8 * 4 can not be written as 84, because 84 can be means as 80 + 4, meanwhile, 8 * 4 is 8 + 8 + 8 + 8 = 32.
Let’s try another example, assume we have format operations like (2+3)^2 = 25, we are using some specific value of numbers, which is 2 and 3, and the results will always be 25. On the other hand, if we are using some other alphabetical symbols, let's say we use an “x” which mean can become any value of numbers and we also use a “y” that also can be any value of numbers that different from an “x”, then we will have some sort of mathematical form like (x+y)^2 = x^2 + 2xy + y^2, in which, we will call this mathematical form as an equation.
The most important thing in this equations (x+y)^2 = x^2 + 2xy + y^2 is the equation showing us general relations that can also happen almost to a wide range of values. If we try to make an exchange for a symbol of “x” into a value of numbers like 3 and for the “y” we exchange with the value of 5, then we will get (3+5)^2 = 3^2 + 2*3*5 + 2^2 = 43. Or we also can exchange the alphabet symbol of “x” with the value of the number of “7” and “y” with the value number of “11’, which will give us a result as (7+11)^2 = 7^2 + 2*7*11 + 11^2 = 324.
Algebra, a mathematical method from any kind of numbers and variables operations, discussing with much more detail the connection among those numbers. in general, algebra only gets a special connection with some format, as much as those formats came from a fundamental format that has been applied generally. Algebra has also been using for solving several kinds of cases in which we can start with the value of 1 or some other variant of number value along with the variables that we don’t know their actual value then we symbolically it by the algebra symbols methodology.
To be continued with information about Algebra from the Ancient and their Law.
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