Turn on thread page Beta
    • Thread Starter
    Offline

    11
    ReputationRep:
    I was watching a maths video and the person claimed 1/0 was infinity, but I heard something is only infinite if it approaches infinity, despite the Google dictionary defining infinite as 'limitless or endless in space, extent, or size; impossible to measure or calculate'. No amount of 0s will ever reach 1 (zero is nothing!) So surely 1/0 is undefined, and does anyone know if it does need to approach infinity to classed as infinite?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Al4stair)
    I was watching a maths video and the person claimed 1/0 was infinity, but I heard something is only infinite if it approaches infinity, despite the Google dictionary defining infinite as 'limitless or endless in space, extent, or size; impossible to measure or calculate'. No amount of 0s will ever reach 1 (zero is nothing!) So surely 1/0 is undefined, and does anyone know if it does need to approach infinity to classed as infinite?
    You can't say anything *is* infinite because infinity is not a number. The best you can do is use the phrase 'tends towards' when talking about limits and so we get that \dfrac{1}{x} \rightarrow \infty as x \rightarrow 0
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by RDKGames)
    You can't say anything *is* infinite because infinity is not a number. The best you can do is use the phrase 'tends towards' when talking about limits and so we get that \dfrac{1}{x} \rightarrow \infty as x \rightarrow 0
    Yes, so can you say 1/0 tends to infinity, because it never approaches infinity?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Al4stair)
    Yes, so you can you say 1/0 tends to infinity, because it never approaches infinity?
    This statement doesn't make sense.

    For one, you used 1/0 which is an undefined quantity. It doesn't tend to anything.

    Secondly, since you want to talk about 1/x instead as x \rightarrow 0, the phrases "tends to" and "approaches" are interchangeable. So your statement is the same as saying "1/x tends to infinity because it never tends to infinity" and clearly you can see how this doesn't make sense.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by RDKGames)
    This statement doesn't make sense.

    For one, you used 1/0 which is an undefined quantity. It doesn't tend to anything.

    Secondly, since you want to talk about 1/x instead as x \rightarrow 0, the phrases "tends to" and "approaches" are interchangeable. So your statement is the same as saying "1/x tends to infinity because it never tends to infinity" and clearly you can see how this doesn't make sense.
    No. I am talking about 1/0. I don't know why you are using x as if the denominator is a variable, it is not. But anyway according to what you written, x=0 in what I am looking at (you said 1/x).

    You said 'the phrases "tends to" and "approaches" are interchangeable', I understand this and never implied otherwise.

    I never at all said "1/x tends to infinity because it never tends to infinity" (again x=0 ...). If you read my post, I am specifically stating otherwise and exactly said that 1/0 is an undefined quantity.

    So to re-iterate. I read online of someone claiming that 1/0 has an infinite answer. This matches the definition which states that infinite means 'limitless or endless in space, extent, or size; impossible to measure or calculate' as an endless amount of zeroes would have to be used (but will never reach 1, which brings me onto the point of the question). As no amount of zeroes will ever make up 1, 1 divided by 0 surely does not have an infinite amount of answers. HOWEVER, this would require the definition of infinite to include that for something to be classified as infinite, the value must approach (or tend to, once again I do understand they are synonymous). However the definition of infinite mentioned previously (limitless or endless in space, extent, or size; impossible to measure or calculate) does not include this clause.

    So to summarise, and the main reason why I made this post is to ask, for something to classified as infinite, does the value involved have to approach infinity, or does an endless amount of the value have to be used (or try to be used) to reach infinity as in the case of 1/0?
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Al4stair)
    ...
    As I said, 1/0 is not infinity. You may say it is infinity in context for the sake of understanding a concept at hand, but you cannot say \frac{1}{0}=\infty generally because infinity is not a number.

    Just because 1/x tends to infinity as x tends to 0, it does not imply that 1/x *is* infinity at x=0
    Offline

    15
    ReputationRep:
    (Original post by RDKGames)
    You can't say anything *is* infinite because infinity is not a number. The best you can do is use the phrase 'tends towards' when talking about limits and so we get that \dfrac{1}{x} \rightarrow \infty as x \rightarrow 0
     1/x\rightarrow -\infty as  x\rightarrow 0^- .
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by B_9710)
     1/x\rightarrow -\infty as  x\rightarrow 0^- .
    Yes, I thought about mentioning this but decided not to in the end.
    Offline

    3
    ReputationRep:
    In Hausdorff space if \displaystyle \lim_{x \nearrow a}f \ne \lim_{x \searrow a} f then f is undefined at a. None more need be said!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 2, 2018

1,111

students online now

800,000+

Exam discussions

Find your exam discussion here

Poll
Should predicted grades be removed from the uni application process
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.