Is it correct or incorrect to say that 1/0 is infinity?

Y

YoungGenius

New member
So, it's like you can't divide 1 by 0, so 1/0 is undefined, that's what I think. Now when you take it as a limit, i.e. approaching 0 from positive direction of X-axis would give us the answer positive infinity whereas approaching 0 from negative direction of X-axis would give us the answer negative infinity. So, then why do people say that 1/0 is infinity? I mean many teachers(I study in a bad school and the teachers there are also bad, so it is not surprising that they teach wrong things) also say this. It should actually be undefined and if you take it as a limit, the answer would be either positive infinity or negative infinity. Or is it like this that the ones who say that 1/0 is infinity mean both positive and negative infinity by saying so? I mean they use the term infinity to mean both positive infinity and negative infinity. But that seems wrong, if it is negative infinity one should really specify it.

So, please help. I hope you understood my question. And if you think my way of deducing things in the above is wrong, then please do let me know. Thanks!
 
A

AwmsA

New member
Actually, the answer is a little hairy. Using the standard definition of division, the statement 1/0 doesn't even make sense.

Short answer: Without more context, the division by zero is undefined.

Little longer answer (see my post in the link):
http://answers.yahoo.com/question/index;_ylt=AupT5Cp8CGnrovtI_UToOrfsy6IX;_ylv=3?qid=20090215154631AA76Ihs&show=7#profile-info-1Hteawwmaa
 
V

Victor

Member
The classical approach is to consider the meaning of division. For example, 20/4 can be interpreted as "how many time do we need to subtract 4 from 20 to reduce it to zero?" The answer is 5.

Apply this to your problem; "how many times do we need to subtract zero from 1 to reduce it to zero?"

The answer is "a very very large number of times that cannot be counted because the subtraction has no effect on the initial number."

For a negative number, the process is the same but requires addition instead of subtraction. So (-20)/5 needs -4 subtractions.

The concepts of plus-infinity and minus-infinity have no meaning, even if you wish to consider (-1)/0, except it is sometimes useful to consider the value of the initial number. The answer is still the same.
 


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