Editing 2687: Division Notation
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 10: | Line 10: | ||
==Explanation== | ==Explanation== | ||
− | + | {{incomplete|Created by a GROUP OF SCHOOLCHILDREN DIVIDED AMONGST THEMSELVES. Do NOT delete this tazg too soon.}} | |
− | + | ||
− | |||
This comic pokes fun at some of the ways to write the {{w|Division (mathematics)|division}} operation in math. In this comic, [[Randall]] has used A as the dividend (the number being divided) and B as the divisor (the number that A is divided by). Division is the fourth simplest arithmetic operation in mathematics, after addition, subtraction, and multiplication.[https://plato.stanford.edu/entries/principia-mathematica/#PartIVRelaArit] | This comic pokes fun at some of the ways to write the {{w|Division (mathematics)|division}} operation in math. In this comic, [[Randall]] has used A as the dividend (the number being divided) and B as the divisor (the number that A is divided by). Division is the fourth simplest arithmetic operation in mathematics, after addition, subtraction, and multiplication.[https://plato.stanford.edu/entries/principia-mathematica/#PartIVRelaArit] | ||
The first two of the seven notations shown are the {{w|division sign}} (÷) and the {{w|long division}} notation used for {{w|short division}} and {{w|long division}} in beginning arithmetic. (Note: division typography is only used in some countries, and there are [https://en.wikipedia.org/wiki/Long_division#Notation_in_non-English-speaking_countries different notations in the non-English speaking world]). These methods of division are often used by school children because the ÷ sign is what most people use when first learning division, and the short division format is usually the first algorithm learned for dividing arbitrary dividends, typically starting with the easier abbreviated short division form. | The first two of the seven notations shown are the {{w|division sign}} (÷) and the {{w|long division}} notation used for {{w|short division}} and {{w|long division}} in beginning arithmetic. (Note: division typography is only used in some countries, and there are [https://en.wikipedia.org/wiki/Long_division#Notation_in_non-English-speaking_countries different notations in the non-English speaking world]). These methods of division are often used by school children because the ÷ sign is what most people use when first learning division, and the short division format is usually the first algorithm learned for dividing arbitrary dividends, typically starting with the easier abbreviated short division form. | ||
− | The expression on the third line, A/B, is the way division is usually written in software code. The four simple arithmetic operations in programming usually are +, -, *, /. This | + | The expression on the third line, A/B, is the way division is usually written in software code. The four simple arithmetic operations in programming usually are +, -, *, /. This one was missing in the first version of the comic. This is most commonly seen in regular mathematics as it somewhat saves space, and is easy to type with the slash key. Additionally, it uses standard {{w|ASCII}} characters instead of sophisticated notation. |
− | The expression on the | + | The expression on the forth line, <sup>a</sup>/<sub>b</sub>, is how division is usually written when typography costs are not in question, in fraction notation. The Unicode character sets provide some specific fractions such as ⅓ as well as some superscript and subscript characters, so someone familiar with it might use it to write fractions such as ²²⁄₇. |
− | The fifth notation is the way division is written in science | + | The fifth notation is the way division is written in science: the dividend on the top of the expression over the divisor on the bottom under a horizontal line. This is how a {{w|Fraction|fraction}} would be written. It has the advantage of clearly separating the numerator and denominator when they are longer expressions, such as polynomials, without needing to add parentheses. This format is mostly used in written and professionally typeset math, as it can't be typed without something like {{w|MathML}}, {{w|LaTeX}} or HTML tables. |
− | The sixth | + | The sixth notation uses a negative exponent. The exponent -1 is equivalent to {{w|Multiplicative inverse|reciprocation}}. It can be used to keep the entire expression on one line. Note that ab<sup>-1</sup> is equal to <sup>a</sup>/<sub>b</sub>. This format is often used to express physical units. |
− | The final form of notation declares a function. The writer defines a new function, F, that takes in the parameters A and B, before listing out the function's definition (trailing off in increasingly smaller text). | + | The final form of notation declares a function. The writer defines a new function, F, that takes in the parameters A and B, before listing out the function's definition (trailing off in increasingly smaller text). Randall warns the reader they should escape while they still can, because both the function itself and the math environment as a whole are going to get relatively tedious. Integer division can be defined in terms of multiplicative inequalities and the remainder, or modulo ('%' in Python), operator. This situation is likely to occur in many sorts of algebra, where one might have to define what "division" means for two elements of a mathematical object such as a group, ring, or magma. One example would be an object G, such that, for two elements A and B of G, "A divided by B" is defined as an element C such that CB=A, or alternatively as an element C such that BC=A. These definitions will differ if multiplication in G is not commutative. Furthermore, if such a C is not unique, the function F(A,B) will need to include a method to select a unique value for "A divided by B" for each A and B. Thus, the F(A,B) in the comic might not even refer to a uniquely defined operation, but simply to the property of a function F(A,B) that is a valid division operation on G, given some definition of division. You were warned. |
− | The title text | + | The title text recommends distinguishing ÷ from %. |
==Transcript== | ==Transcript== | ||
− | + | {{incomplete transcript|Do NOT delete this tag too soon.}} | |
− | : | + | :<u>Division notation</u> |
− | + | :A÷B | |
− | + | :B(Ā Schoolchild. | |
− | : | + | :A/B Software engineer. |
− | + | :<sup>A</sup>⁄<sub>B</sub> Normal person or Unicode enthusiast. | |
− | :A/B | + | :A over B Scientist. |
− | + | :AB<sup>-1</sup> Fancy scientist. | |
− | + | :F(A, B) such that F(G)= (text getting smaller) Oh no, run | |
− | : | ||
− | |||
− | |||
− | : | ||
− | : | ||
− | |||
− | |||
− | |||
− | |||
− | :F(A, B) | ||
− | |||
{{comic discussion}} | {{comic discussion}} |