Draft:Monkey Math

Monkey math is a joke method of math which replaces the normal Operation (mathematics). It got its name from the fact how Monkeys swing from trees, combining/touching each of them, which is how monkey math is usually done. It is also one way of doing math that makes order matter every time.

Division and subtraction and nth root and etc.

They are not affected by monkey math, so if I said 1+sqrt(2) = 1+1.414... = 11.414... which is basically simplify the number to a decimal or whole then add. You cannot do subtraction in monkey math.

Addition

Doing addition is simple in monkey math. It depends on the order you put the numbers in. For example, if I do 1+1 it would be 2 normally, but in monkey math it would be 11. You would simply remove the plus signs. It changes when the order is different, for example 3+4 = 34 but 4+3 = 43, so order matters. When you do fractional numbers, add the decimal place last and for fractions you convert it to a decimal. For example, 1+2.4 = 12.4, and 2.4+1 = 21.4, which is the same as 2+1+.4=21.4 and the same goes for more decimals like 1+2+3.4+4.5 = 1+2+3+4+.4+.5 = 1234.45, and for irrational numbers like 2.5+pi = 23.51415926535... and for pi+2.5 it is 32.(endless decimal places of pi)5. Also for adding 0 you do the same thing, 1+0 = 10 and 0+1 = 01=1.

Multiplication

Multiplication is pretty similar to addition. You would make it into addition again. For example, if you do 5*4, that is the same as saying 5+5+5+5=5555. Once again order matters so 4*5 = 4+4+4+4+4=44444. It is the same for decimals so 4.3*2 = 4.3+4.3 = 44.33, and 2*4.3 = 2+2+2+2+0.6 = 2222.6

Exponents and tetration and beyond

For exponents you simplify it to multiplication then addition. So 4^3 is 4*4*4 = (4+4+4+4)*4 = 4444*4 = 444444444444. Another way to think about it is multiply the big and small number then thats how many you would do, so 5^6 = 5*6 in normal math 5's, which is 55555555... until you have 30 fives. With fractional exponents evaluate the root then do to the power of, so 8^2/3 = (cbrt(8))^2 = 2^2=2*2=2+2=22. Tetration is the same you make it into exponents then multiply then add. So 2 tetrated to 3 = 2^2^2 = 2^(2*2) = 2^(2+2) = 2^(22) = 2*2*2*2*2*2... which is 2+2+2+2, to make this easier we can do the multiply trick so 2*22 normally is 44, so 2 tetrated to 3 in monkey math is 222222222... (44 number 2's). Its the same for Pentation and more, go to Tetration then continue.

Summation

With summation it is very easy to do because summation is literally just lots of addition. So an example is $\sum _{n=1}^{5}3n$ which is adding the numbers 1 to 5 but they are multiplied by three for each, so we get 3+6+9+12+15 = 3691215. The same is for the multiplication variant of summation $\prod _{n=7}^{9}n$ = 7*8*9 = (7+7+7+7+7+7+7+7)*9 = (lots of number sevens).

Complex numbers

Adding complex numbers is very simple also. If I wanted to add 2+i+4 you would sort it out to be in the form a+bi, so 2+i+4 = 24+i. Another example is 4.6i+12+9i+3 = (12+3)+(4.6i+9i) = 123+49.6i. For multiplication like (4+2i)*(1+2i) = (4*1)+(4*2i)+(2i*1)+(2i*2i) = 4+2i+2i+2i+2i+2i+4i+4i+4+1i+1i = 44+222224411i. That may look hard but all you have to do is multiply like distribution, and for the 2i*2i is (2*2)+(2*1i)+(2*1i)+(1i*1i) = 22+11i+11i+1i. I may have made a mistake there so correct me if im wrong. Remember there is a coefficient of 1 next to every imaginary number.

Integrals

For integrals we cannot do the exact area under the curve. Instead we can use a Riemann sum to get a finite number for the result. This is because if we did normal integration, and integration is technically just a infinite sum, adding those sums with monkey math would get you an infinitely big number. So we can only really use an approximation. So with that an example would be $\int _{1}^{2}\left(2x\right)dx$ then say right/left/middle/etc riemann sum then turn it into a summation problem then evaluate it.

Factorials

For factorials we all know it is just multiplication. Remember that it is in descending order (largest number first). However for fractional factorials it is the same as the gamma function minus one. For example 2.3! = $\Gamma (1.3)$ which then is an integral so from before say right/left/etc riemann sum then evaluate it. It will be a long process but it will be worth it in the end.

History

I dont know (please someone find a citation before this article gets thanos-snapped from existence)