Difference Between Infinity and Undefined

Infinity vs Undefined

‘Infinity’ and ‘undefined’ are two different concepts. These are more frequently used concepts in many fields, especially in Mathematics and Physics.

Infinity

What is the largest number that you can imagine? Whatever the number you pick, one can introduce a number larger than the number you pick by simply adding one to that. The concept ‘infinity’ could have been introduced as an answer to this question. The term ‘infinity’ comes from a Latin “infinitas”, which means “unboundedness”.

There is no number larger than infinity. However, infinity is not the largest number, because it is not a number.

What is the exact value of infinity? Let us answer this question after considering this example.

In set theory, the set of natural numbers, set of integers, and set of real numbers are said to be infinite sets, because all these sets contain infinitely many numbers. It is clear that set of real numbers contain more elements than in the set of integers. In other words, it is possible for one infinite set to contain more elements than another infinite set.

Therefore, it should be clearly understood that the concept of infinity varies depending on the subject area that we are talking about. Infinity has various applications in mathematics; in set theory, calculus and so many other fields.

Undefined

What is the value when you divide any number by zero? Is it infinity? If you are physicist, it can be zero depending on the theory you are applying it. However, if you are a mathematician, it is undefined.

For another example; what would be the logarithm of a negative number? Since we cannot find a number x, such that n^x= -r, where n and r are integers; we would say the logarithm of a negative number is undefined.

Mathematically, “undefined” can be defined as an expression which is impossible, or an expression which does not have an exact definition, or an expression that cannot be interpreted. However, something that is undefined today, may be given a definition in the future. For example, square root of a negative number was undefined. In modern mathematics, the square root of -1 is defined as imaginary number i.

What are the values of ‘infinity-infinity’ and ‘infinity/infinity’? All these are still undefined. The value of infinity is also undefined.

What is the difference between Infinity and Undefined? • Undefined means, it is impossible to solve. • Infinity means, it is without bound.