What is the Riemann sphere used for?
As with any compact Riemann surface, the sphere may also be viewed as a projective algebraic curve, making it a fundamental example in algebraic geometry. It also finds utility in other disciplines that depend on analysis and geometry, such as the Bloch sphere of quantum mechanics and in other branches of physics.
Why is a number divided by 0 undefined?
The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction. r*0=a. (1) But r*0=0 for all numbers r, and so unless a=0 there is no solution of equation (1).
What happens when a computer divides a number by zero?
So, when something is divided by zero, mathematicians simply state that the answer is ‘undefined’. This is not a totally abstract idea as you can see it in action in the real world. Computer programmers who accidentally divide by zero will get their code stuck in an infinite loop, for instance.
Why is projective geometry important?
In general, by ignoring geometric measurements such as distances and angles, projective geometry enables a clearer understanding of some more generic properties of geometric objects. Such insights have since been incorporated in many more advanced areas of mathematics.
What is a sphere in math?
sphere, In geometry, the set of all points in three-dimensional space lying the same distance (the radius) from a given point (the centre), or the result of rotating a circle about one of its diameters.
What does undefined mean in math?
An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the field of real numbers.
Why is it impossible to divide by zero?
These notes discuss why we cannot divide by 0. The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1. Arithmetic starts by assuming there are objects called real numbers.
Is infinity a number?
Infinity is not a number. Instead, it’s a kind of number. You need infinite numbers to talk about and compare amounts that are unending, but some unending amounts—some infinities—are literally bigger than others. When a number refers to how many things there are, it is called a ‘cardinal number’.
How do you divide by zero?
Ans: Dividing any number by zero does not make sense, because in maths, dividing by zero can be interpreted as multiplying by zero. There’s no number that you can multiply by zero to get a non-zero number. There’s no solution, so any non-zero number divided by 0 is undefined.
What is the result when zero is divided by zero?
undefined
So, that means that this is going to be undefined. So zero divided by zero is undefined.
Can you divide 0 by a number?
It is well known that you cannot divide a number by zero. Math teachers write, for example, 24 ÷ 0 = undefined. They use analogies to convince students that it is impossible and meaningless, that “you cannot divide something by nothing.” Yet we also learn that we can multiply by zero, add zero, and subtract zero.