Infinity & undefined

This is to clear the confusion over the answer given by a mathematics lecturer to Justice Markandey Katju (on what is one divided by zero) and the letters in response to the article “Professor, teach thyself” (Sept. 3). In mathematics, anything divided by zero is not defined (and not infinity). But ‘limit’ (1/x); x->0 is well defined and is equal to infinity (it is the basic concept of limits).

Now this statement is most commonly (though not correctly) referred to as 1/0 = infinity and is so common in mathematics and physics that people working/studying in this field take limits to be obvious. This is what the lecturer might have had in mind. In any case, the intellect of a person cannot be tested by posing one question to him.

Ravi Mohan,


In mathematics, expressions like 1/0 are undefined. But the limit of the expression 1/x as x tends to zero is infinity. Similarly, expressions like 0/0 are undefined. But the limit of some expressions may take such forms when the variable takes a certain value and these are called indeterminate. Thus 1/0 is not infinity and 0/0 is not indeterminate, since division by zero is not defined. When something is not defined, one should not ask what its value is.

Justice Katju deserves all praise for voicing his concern over the education system prevailing in India. But it appears that he does not know the distinction between the concepts of infinity and indeterminate. It would be better for such persons to avoid saying things like ‘he was unfit to teach even in an intermediate college.’ Please do not underestimate the calibre of professors.

P. Sundaram,


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Printable version | Jul 17, 2021 11:55:41 PM | https://www.thehindu.com/opinion/letters/infinity-undefined/article3863329.ece

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