What is 0 / 0
Let us think how division and multiplication works.
If 100/2 = 50 then 2 * 50 = 100
If 100/4 = 25 then 4 * 25 = 100
If 100/5 = 20 then 5 * 20 = 100
If 100/0 = ? then 0 * ? = 100
What should be in replace of ? which given the result 100. Here we can not defined it so the answer of 100/0 is undefined.
Now if question is about 0/0
If 0/0 =? then 0 * ? = 0
There may be any number 0, 1, 2, 3, ... Its mean any number can be put in replace of question marks(?). This is not a single number. These number may be 0, 1, 2, 3 ...
So it is indeterminate.
Suppose question is about a/b=?
When a = 3 and b= 3 then 3/3 = ?
Let here 'a' are apples and 'b' are boys.
Its means you have 3 apples for distribute among 3 boys.
When a = 0 and b= 3 then 0/3 = ?
How much boys will get. Clearly show that each boy get one apple so 3/3 = 1
Its means you have 0 apples for distribute among 3 boys.
When a = 3 and b= 0 then 3/0 = ?
How much boys will get. Clearly show that they get zero apples so 0/3 = 0
Its means you have 3 apples for distribute among 0 boys.
When a = 0 and b = 0 then 0/0 = ?
Here the situation is there is no any boys to get apples. Here the quesion has no sence. It is not defined. So it is undefined.
Its means we have 0 apples for distribute among 0 boys or we have to distribute nothing in nothing.
How many apples will get each boy (who is zero boy)?
Here the situation is you do not have to worry to distribute anything when there is zero apples and zero people to distribute.
If you still worried but you can do nothing. In such case you are facing “indeterminate” term here.
Mathematically is an indeterminate term widely used in calculus mainly in limit calculations and there is a rule called L’hospital rule to calculate those limits .
Difference between Indeterminate, Undefine and Infinity
Mostly are confused about indeterminate, undefined and infinity.
“Indeterminate” means that a particular expression could logically take several different values, and we don’t know which one.
"Indeterminate" has a value which cannot be precisely known. The number of molecules on your fingertip is indeterminate. Surely,it has a finite value but you can't precisely know it.
“Undefined” means that a particular expression can’t logically take any value at all.
"Undefined" does NOT have a value or its just not defined. Value of a real number divided by zero is undefined, in geometry definition of line, point,plane are not defined. These are undefined entities.
"Infinity" is greater than any finite number.It is not a well defined number. Its also means that is never end. For example 10/3=3.333………
Infinity is not a number, it is just a concept. but Undefined means, it is impossible to solve.
Infinity means, it is without bound. It is the idea of something that has no end.
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What is difference between undefined, indeterminate and infinity