there is about 116 universally recognized mathematical symbols and I'm going to explain every one of them addition 1 2 + 1 2 = 1 2 3 4 boom subtraction if 2 + 2 is 4 then 4 - 2 = 2 it's addition just backwards multiplication if I have a 3X3 grid of cells then I have nine cells because 3 * 3 equals 9 Division if Johnny has six apples and two friends how many apples does each friend get three because 6 / 2 is three but you struggle with division because you have no friends and you can't divide by zero plus plus minus we didn't know whether to put a plus or a minus here so we use both 2 + - 1 is 1 or 3 minus plus a + - B minus plus Cal a plus B minus C or a minus B plus C these signs remain opposites equal if a equals b means a is the same as B then a not equals b means a is not the same as B but we can get more specific than that we can write a is greater than b or a is less than b and we can even put a little line here to indicate that a is greater than or equal to B percent literally just means the exact same thing as divide by 100 so if you're dealing with a difficult percentage problem then try moving the percentage sign around because it doesn't actually matter where the percent sign goes and you can easily find the answer degrees 360° is one full turn so one degree is a teeny tiny turn but you know what's even smaller than 1° an arcc which is 1° divided by 3,600 Powers the nth power of a is just a * a * a * a n * and the nth root of a is the inverse of this so the nth root of the nth power of a is just a again same thing just backwards Pi Dr Edward J Goodwin an amateur mathematician from Indiana claimed to have discovered a method for squaring the circle a famous problem that had already been proven unsolvable in 1882 despite this Goodwin was convinced of his own work and saw official recognition for his discoveries but rather than publishing a mathematical Journal like the rest of us he took a different approach he tried to make it State Long in 1897 house bill number 246 was brought to the Indiana General Assembly the bill effectively claimed to fix the value of pi the ratio of the diameter and the circumference is as 54s to 4 which implies that Pi is 3.2 amazingly the Indiana House of Representatives unanimously passed the bill on February 5th 1897 most likely because they saw it as a way to support Indiana's reputation in education and science the bill was then sent to Indiana Senate for final approval by sheer look Professor Clarence Waldo was visiting the Indiana legislature on unrelated business and when he heard about the bill he was horrified and immediately stepped in he had to explain to the house that one the bill is mathematically incorrect two it would make Indiana the laughing stock of the world and three mathematical constants like Pi can't be legislated or in other words just because Indiana says Pi is 3.2 doesn't mean Pi is 3.2 eventually Indiana had to accept the fact that Pi was not 3.2 but it makes you think what if if they did it Delta typically means difference for example the gradient of a straight line is the difference between the two y-coordinates over the difference between the two x coordinates or Delta y over Delta X proportional if Y is proportional to X then y equals KX where K is a constant sometimes you might see a proportional sign flipped to indicate that Y is inversely proportional or y equal K overx approximately equal I actually already Ed this for my value of pi because no matter how many decimal places you add you can never actually write down the exact value of pi it will only ever be approximately equal perpendicular two lines are perpendicular if they intersect at a right angle parallel two lines are parallel if they're in the same plane and never intersect no matter how far they extend angle sometimes measured in degrees but can also be measured in radians where a full turn is 2 Pi similar a is similar to B when a is the same shape but different in size you can also put a line under it to make it similar or equal congruent a is congruent to B if they have the same shape and size the to Arrow is used for a range of things from vectors to limits to mappings but it generally always means to the line symbol shows an infinite set of points extending in both directions without any end points width or thickness therefore because the absolute value of a number is the difference between that number and zero on a number line the floor of a number is the value of that number rounded down to the nearest integer and the ceiling is the value rounded up to the nearest integer the factorial of n gives you the number of ways of arranging n elements so the number of ways of arranging a deck of cards is 52 factorial or 8 * 10 the 67 for reference the number of grains of sands on Earth is 7.5 * 10 18 Sigma is typically used to talk about the sum of many terms the initial index is defined below the sigma and the final index is above and the terms to be summed is on the right of the sigma also sometimes Sigma can be used to define the set of letters product works in the same way as Sigma or with multiplying instead of adding contrary to popular belief Infinity actually isn't the biggest number because Infinity isn't a number infinity is a concept that means unboundedness Al if null is the smallest infinity and Omega is the biggest Little D like Delta represents the change or difference in something but when we're dealing with curved lines the only way to find the exact gradient is to make the change in X and the change in y infinitely small we represent this using Little D partial is almost the same as Little D but we use Little D to find the derivative and partial to find the partial derivative which calculates the rate of change with respect to one variable while keeping all the other variables constant in a function with multiple variables integral calculates the area under a curve by adding together all the thin slices which make up the area it's an elongated version of the letter s which stands for sum and it's also the inverse of differentiation set theory curly braces Define a set as a list of its elements the most common sets are the natural numbers the integers the rational numbers the real numbers the complex numbers and the prime numbers and you can also say it's reigning if and only if there is water coming out of the sky one is an element of the set 1 2 3 because one appears in the set but four is not an element of the set one 2 3 a union b is all the elements in the set a or b and a intersect b is all the elements in set a and b a is a subset of B if all the elements in a are also in set B you can also put a line under the subset sign to signify that it's subset or equal to this gun symbol means not and a backslash means the set difference which means all the elements in a that's not in B and it looks like this this means and and this means all this means for all and this means there exists curly p is used to denote the power set and the power set of a is just the set of all possible subsets of a so if a is one two then the power set of a is the empty set the set of one the set of two and the set one two a colon is used to represent such that or given and you can also use a vertical line so for example the power set of a is just the set of all s such that s is a subset or equal to a the empty set is represented by the Danish o slash symbol and Omega is used in probability Theory to represent the set of all possible outcomes I is equal to the < TK of minus1 so i^ 2 is -1 and I 4 is -1 * -1 which is just 1 the do product of two vectors A and B where a is 1 2 - 3 and b is 4 - 5 6 is the sum of the product of the adjacent values so so you just multiply the 1 by the four and then the 2 by the Min -5 and the -3 by the 6 which gives you 4 - 10 - 18 which is - 24 if a is 1 2 and B is a b then the cartisian product is the set of ordered pairs 1 a 1 b 2 a 2 B so the cartisian product of A and B is the set of all pairs of elements where the first is in a and the second is in B if f and g are functions then F Circle G is the composite of the functions f and g so you find G of X first then you find F of all of that the mean represented by mu is the average of a data set which is found using this formula or as I like to say the sum over the count the standard deviation denoted by Sigma is how spread out the data is so if you find the mean using this formula then you find the standard deviation using this to is just 2 pi which some believe makes it easier to work with circles so instead of finding the circumference using 2 pi r you just use to r or instead of finding the area using p Pi r^ 2 you just use to r^ 2 / 2 okay maybe not that one but teren Tower is pretty cool the golden ratio is 1 +un 5 / 2 or 1.618 the Raymond zeta function equals the sum from 1 to Infinity of 1 / n the S and it's also the product of 1 - 1/ P to the S inverted for all prime numbers so this is useful when working with prime numbers called Hit is the set of all quarians and a querian is a number Q which equals a plus b i+ CJ plus DK where I 2 = = J2 = k^2 = i j k = minus1 so i j = k j k = i and K IAL J got it bold m is the set of all matrices and a matrix is just a grid of numbers more on that later if a is a square Matrix and X is a non-zero Vector then the igon value satisfies this equation a sequence space is a set of sequences that satisfy specific conditions for example if L Infinity is the space of all bounded sequences then sequence x subn = -1 the N belongs to L Infinity because X subn is bounded between minus1 and 1 the Y Strauss elliptic is this formula here and it's used in complex analysis but it's not used in hippopotamus so honestly it's not worth my time and that's definitely not because I don't understand it this funny symbol just means section for example c section 4.2 for proof and if Z equal a plus bi I then the conjugate of Z equals a minus bi core product is the opposite of the cartisian product so if the cartisian product joins the elements of A and B together then the core product keeps them disjointed nabla is used to denote the gradient of a function as a vector which points in the direction of steepest increase in that part of the function so if FAL x + 2 y + 3 Z then nabla f = 1 2 3 if a precedes B then a is in some way of lower order than b but it doesn't necessarily mean that a is less than b for example we can write the set one precedes the set one two because one two has more elements but that doesn't necessarily mean that one is less than one to instead of saying that piano's instead of saying that from piano's axioms we can prove 1+ 1 is 2 we can just say that piano's axioms entails 1+ 1 is 2 so the statement gamma entails f means that fi is provable from the set of assumptions gamma semantic entailment just means that fi is true in all models where the assumptions gamma whole Al if null is the smallest countable infinity and it's equal to the size of the set of natural numbers the size of the set of real numbers is two to the power of Alf null Beth null equals Alf null which is the size of the set of natural numbers Beth one equals 2 to the power Beth null which is the size of the set of real numbers and Beth 2 equals 2 to the power Beth one which is the size of the power set of the real numbers so in general Beth n + 1 equals 2 to the Beth n if R is the table with columns employee ID name and Department ID and S is the table with columns Department ID Department name then R join s is the table with columns employee ID name Department ID and Department name the department IDs just get joined together into one table so if a is this 2x two Matrix here then the conjugate of a is the complex conjugate of each of the values in a and a transposed is what happens when you take the rows of Matrix a and turn them into columns a dagger is what happens when you do both and it doesn't matter which way around you do them double dagger is used as a custom operation and it can mean anything and Diamond p is possibly P if V is the vector 1 2 and W is the vector 345 then to find the tensor product of the two vectors you lay the first Vector along the side and the second along the top and then multiply the the rows by The Columns to find the cells in the resulting Matrix if a and b are matrices then the hadamar product of A and B is just the element wise product of each element in the Matrix the symmetric difference of A and B is a subtract B Union B subtract a and it looks like this the top symbol is used to mean always true for example P or not p is always true and the bottom symbol means always false for example p and not p is always false the gamma function is this function here and it helps us to build a continuous function for the factor of n the Kai symbol is used in Oiler characteristic which is vertices minus edges plus faces and it's equal to two for all threedimensional polygons Kappa stands for curvature and it's found using this equation the Foria transform takes a function and breaks it down into the sum of s and cosine waves of different frequencies the laass transform takes a function of time and converts it into a function of a complex variable making it easier to solve differential equations a Hilbert space is like an extended version of 3D space but it can have infinitely many dimensions and applies to functions signals and complex numbers here's a meme to explain how it works Epsilon is used in the definition of limits think of it as a very small number which represents how close you want the function's output to get to a certain value in topology curly n denotes the neighborhood of a point P which is a set containing All Points close to p and curly T represents a topology where a mug equals a donut curly M represents a manifold which is a space that looks like regular ukian space locally but can have complex properties GL globally in Game Theory curly a represents the set of actions decisions or strategies available to a player if a has igen values Lambda 1 Lambda 2 Lambda 3 and so on then a equals P Lambda inverse P where p is the Matrix of igen vectors and Lambda is the diagonal matrix of igon values in complex analysis P denotes the complex potential or special function such as the Dima function which is defined as the derivative of the log of the gamma function click on this video if you want to see more and piss off finally finally it's over yes yes