[Max/Jeremiah]

by Guest Tue Sep 04, 2012 9:27 pm

What is the correct answer if someone asks 'what is one divided by zero equal to?'

by MaxEntropy_Man Tue Sep 04, 2012 9:32 pm

it's equal to republican budget math. haha.

but seriously, it doesn't make sense to ask what is any finite number (one in your case) divided by zero. it is not defined. what you can say is that the limit of one divided by a number made arbitrarily small, approaches infinity.

by Guest Tue Sep 04, 2012 9:38 pm

MaxEntropy_Man wrote:it's equal to republican budget math. haha.

but seriously, it doesn't make sense to ask what is any finite number (one in your case) divided by zero. it is not defined. what you can say is that the limit of one divided by a number made arbitrarily small, approaches infinity.

Who is right here and who is wrong?

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Since the teacher was present in court I asked him how much one divided by zero is equal to. He replied, “Infinity.” I told him that his answer was incorrect, and it was evident that he was not even fit to be a teacher in an intermediate college. I wondered how had he become a university lecturer (In mathematics it is impermissible to divide by zero. Hence anything divided by zero is known as an indeterminate number, not infinity).

http://www.thehindu.com/opinion/op-ed/article3851415.ece

But then:

http://www.thehindu.com/opinion/letters/article3855531.ece

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should one say the answer is 'undefined' instead of 'indeterminate' and is there a significant difference in this context between the words 'undefined' and 'indeterminate'.

by MaxEntropy_Man Tue Sep 04, 2012 11:28 pm

your latest post just sounds like a matter of semantics. i think undefined and indeterminate is a distinction without a difference.

1/0 is not a number. however, we can say that:

1/x approaches infinity asymptotically as x approaches 0.

by Guest Tue Sep 04, 2012 11:48 pm

MaxEntropy_Man wrote:your latest post just sounds like a matter of semantics. i think undefined and indeterminate is a distinction without a difference.

1/0 is not a number. however, we can say that:

1/x approaches infinity asymptotically as x approaches 0.

strange to see someone being viciously attacked for saying what you are saying:

http://www.firstpost.com/india/the-hindus-readers-find-katjus-foot-in-his-mouth-443248.html

by MaxEntropy_Man Wed Sep 05, 2012 6:01 am

i'd like to add a bit more to what i said. what i said about the limit of 1/x is strictly true for x approaching zero from above. when x approaches zero from below the limit of 1/x approaches negative infinity. so in fact the answer to the question what is the limit of 1/x as x approaches zero is indeed undefined (or doesn't exist), because the limits from above and below don't match, i.e. the answers diverge on either side of the real axis.

see what i mean in this wolfram alpha question i created:
http://www.wolframalpha.com/input/?i=limit+x+approaches+zero+1%2Fx

by contrast, a function like 1/x^2 has a well-defined limit since the limit is infinity on both sides of the real axis.

see here:
http://www.wolframalpha.com/input/?i=limit+of+1%2Fx%5E2+as+x+approaches+zero

so in fact katju is more correct than the people criticizing him.

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