Most of us give these answers when we are asked the questions. But what is undefined and what is undetermined?. Do they mean the same thing?. We often mistake them as the same. But there is a difference.The two terms have their own definitions.
The concept of 'undefined' and 'undetermined' is mainly found in calculus, a branch of mathematics."Undefined" refers to something which has no definition or does not follow mathematical rule.We know that a certain mathematical expression gives a fixed value. Whatever the condition around us is and wherever it is done, an expression can give the value when it is defined or follows the definition of mathematics. According to the definition, a certain expression can give only one value. But in the case when something is divided by zero, we get two results i,e t∞ and - ∞. When a number is divided by positive numbers, the smaller the value of divisor, the larger the quotient is. As a result , the more the divisor approaches to zero, the quotient approaches to t∞. Again when the number is divided by negative numbers, something happens. It approaches t∞. We get these result when we place them in a number line. So, somethings is divided by exactly zero, the value is t∞. Here we find two results and we know them. They can also be proved . But from a mathematical expression we can find only one result. So, it is not defined as the definition is known to us. It is undefined.
"Undetermined" has values which cannot be precisely known. When we go to prove the expression, it gives so many results but we do not know which is the actual results or for which we can determine the expression. Say, when zero is divided by zero, what happens? some mathematicians said it will be one as some digit gets divided by some one. Some said it will be zero as there is zero as numerator. Some said it will be undefined. But when zero divided by zero, we get many results like, 0,1,2,3,4,.........∞. We know dividend equals to the multiplication of divisor and quotient and anything multiplied by zero is obviously zero.
So,
0 × 0 = 0
0 × 1 =1
0 × 2 = 2
In this way, many results are found. But we do not know for which value it can be determined. And this is undetermined. "Undetermined" is "undefined" too as it does not follow mathematical rules. During addition, subtraction, multiplication or division, the expression which gives more than one value but we know those that is undefined but which gives many values and actual result cannot be determined is known as undetermined . Here we can differentiate.
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There are many other examples like &-& 0° , 0° (subtraction of infinity, zero to the power zero, infinity to the power zero) etc. Which create confusion among us.
In the field of mathematics, we deal with various terms that seem almost same but they are different. Knowing about them is very much interesting and increases our eagerness more and more we go through them. "Undefined" and "Undetermined" are that kinds of terms those have mystery and our mathematicians are always curious to know them.
