Thread: Reducing mathematical operations to addition and subtraction

is it possible to reduce any mathematical operation to a process of simply adding something

for instance,
mulitiplication can be reduced to addition
e.g.
2*3 = 2+2+2

division
e.g.
3/2 = 3*1/2 = 0.5+0.5+0.5

exponents
e.g.
2^3 = 2*2*2=2+2+2+2

is calculus, geometry, linear algebra, stochastic calculus etc. in the end nothing else then addition or subtraction of numbers in a systematic way?

i believe it is, this is how computers/calculators work as they can't divide etc.
for example the trigonometric functions are programmed into a calculator as a mclaurin series. which is the addition of many terms.

however i don't see why you would want to reduce all functions to addition apart from computer programming, the functions are used to make life easier for us.

Not really sure, but at least some operations will be tricky. For instance, how to write the operation "take the square root of x"? Only with an infinite series, thus an infinite number of addition.

Originally Posted by evariste.galois

is it possible to reduce any mathematical operation to a process of simply adding something

for instance,
mulitiplication can be reduced to addition
e.g.
2*3 = 2+2+2

division
e.g.
3/2 = 3*1/2 = 0.5+0.5+0.5

exponents
e.g.
2^3 = 2*2*2=2+2+2+2

is calculus, geometry, linear algebra, stochastic calculus etc. in the end nothing else then addition or subtraction of numbers in a systematic way?

No.

Originally Posted by DrRocket

Originally Posted by evariste.galois

is it possible to reduce any mathematical operation to a process of simply adding something

for instance,
mulitiplication can be reduced to addition
e.g.
2*3 = 2+2+2

division
e.g.
3/2 = 3*1/2 = 0.5+0.5+0.5

exponents
e.g.
2^3 = 2*2*2=2+2+2+2

is calculus, geometry, linear algebra, stochastic calculus etc. in the end nothing else then addition or subtraction of numbers in a systematic way?

No.

ok, could you give an example where it is not possible please?

Originally Posted by evariste.galois

is it possible to reduce any mathematical operation to a process of simply adding something

There is a large class of functions called Holomorphic functions which can be expanded out into a power series. A power series is just a bunch of adding (sometimes with negative coefficients) and calculations of powers.

Here are a few examples of non-Holomorphic functions.
Complex conjugate:
Real Part:

So every mathematical operation can not be turned into just adding but there is a lot that can be done with just adding and the calculation of powers.