The concepts of infinity and indeterminate are taught in classes six and seven. I have been following the discussion on them. But readers seem to confuse students rather than clarify the concepts.
Infinite means “very great, impossible to measure, boundless.” Indeterminate means that “which cannot be calculated exactly.” The term ‘infinity’ is applicable only in graphs — for example, the values in the graph of Sinx go on continuously. If we try to apply the values such as x->infinity in a graph, it shouldn’t have an end point; it should go on continuously. The values such as 1/0, 0/0, etc., are indeterminate. Likewise, 1/0 cannot be calculated by any means including a calculator or computer. Therefore, 1/0 is indeterminate.
This can be understood easily. If there are 0 apples and 3 students, we cannot divide them. Therefore, 0/3=0. If there are 3 apples and 0 students, it is again impossible to distribute them. So, 3/0 is not determined and is, therefore, indeterminate. Conceptually, there is some difference between infinity and indeterminate but when applied, the result is not much different. Whether it is infinite or indeterminate, the value cannot be defined or found exactly.
P. Purvaj Reddy,