Infinity On The Number Line

Calculus Level pending

True or False?

∞ is the number at the end of the real number line. \infty \text{ is the number at the end of the real number line.}

False True

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Zandra Vinegar by Zandra Vinegar

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10 solutions

Devendra Mishra
Jan 31, 2016

Infinity is not an existing number.

11 Helpful 0 Interesting 1 Brilliant 0 Confused

Then, what is? I mean, I've heard (from mathematicians) that is a concept or an idea. But, what is the precise math definition?

I know there are ∞ \infty s bigger than others, but it should't be an obstacle to formalize it. Look at the concept of a number...

Victor Moreno Diaz - 4 years, 10 months ago
Angelo Curcio
Jan 31, 2016

Infinity is more of an idea with no definable value. The number line can stretch to infinity in either direction for example, but the number of points between any two points is also infinite. Just going from 0 to .000000001 has an infinite number of points in between.

Also, if infinity had a definite value, we would have problems like this 2/0=infinity and 1/0=infinity so 2/0 = 1/0 = 15/0 etc.

5 Helpful 0 Interesting 2 Brilliant 1 Confused

Sir, but 11th standard will be using infinity in number line

vijaykrishna vijaykrishna - 1 year, 10 months ago

  1. Take any finite number. Let’s say, 1010. You can get to this number with lower numbers by using the four operations (ex: 1000+10=1010, 1000 < 1010, 10 < 1010). This is not achievable with infinity, which makes it an ‘inaccessible variable’. However, some speculate of other ‘higher’-than-infinity numbers ( ϵ 0 \epsilon_0 ) and a ‘true infinity’ beyond even those.

  • If ± ∞ \pm\infty had a last digit or was at the end, 0.999 … ≠ 1 0.999\ldots\neq1

    • Bao NGUYEN - 5 months, 3 weeks ago

    So you're telling infinity is not defined but the of number line is defined.......Eh ?

    Arjun SivaÞrasadam - 5 years, 4 months ago

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    The end of number line is undefined aswell, because the number line has no end.

    Osher Shukrun - 5 years, 4 months ago

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    Exacty i meant that !!

    Arjun SivaÞrasadam - 5 years, 4 months ago

    End of any line is undefined.

    Shivraj Gondi - 5 years, 4 months ago

    There are multiple infinities, and multiple numbers cannot be in the exact same position on the number line.

    1 Helpful 1 Interesting 1 Brilliant 0 Confused

    Alef naught

    2 Helpful 0 Interesting 0 Brilliant 2 Confused

    Even all the real numbers between 0 and 1 are infinite, so it makes no sense at all to put infinity at the end of the real numbers line.

    1 Helpful 0 Interesting 0 Brilliant 0 Confused

    It the count. the counting means its a number. or there is no infinty in between 1 and zero other that the no:of real no.s in between 1 and zero

    Arjun SivaÞrasadam - 5 years, 4 months ago
    Steve Sybesma
    Apr 11, 2019

    I would have answered YES if you did not draw any numbers between zero and infinity because scale is involved with the way you drew the line. If you draw a number line with zero at one end and infinity at the other, you cannot fill in any other numbers in between, because any number you try to add to the line is virtually at the same spot as the zero. Proportionality would dictate that. The understanding of infinity the person who drew the line was trying to convey is the normal one that most people think of...that infinity is an uncountably large value that encompasses all possible countable numbers.

    0 Helpful 0 Interesting 0 Brilliant 0 Confused
    Rev Ilo
    Oct 11, 2018

    The number line doesn't finish when it "gets" to infinity because it can't get to something that's not a number. Instead we can say that the number line "tends to" the infinity since infinity is the idea that the numbers can always increment by one, no matter how high you're in the number line, it's always possible to increment one.

    0 Helpful 0 Interesting 0 Brilliant 0 Confused
    Shobhit Singh
    Feb 9, 2016

    Actually , Infinity is everywhere on number line . For ex btween 1&2 , between 1&0.1 , between 1&0.000001 . Also , Infinity isn't a number it refers to a endless series .

    0 Helpful 0 Interesting 0 Brilliant 0 Confused
    Ahmed Elselly
    Feb 1, 2016

    it's -1/12

    0 Helpful 0 Interesting 0 Brilliant 0 Confused
    Mayank Bawari
    Jan 31, 2016

    Infinity is not a number, so it can not be distinguished in a number line

    0 Helpful 0 Interesting 0 Brilliant 0 Confused

    so can you show the last number of real numbers !

    The convention is that infinity is a real no:

    Arjun SivaÞrasadam - 5 years, 4 months ago

    I agree that infinity doesn't belong in the real numbers.

    However we are asked if infinity is at the end of the number line. I would say that it is true because there isn't an actual end to the real number line. And soo we can say whatever we want to an impossible situation.

    Diogo Almiro - 5 years, 4 months ago

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    Okay, I've messed up.

    Although it's true (I think) what I said earlier, the question we are asked is Infinity is the number (...) and that is false because infinity isn't a number.

    Diogo Almiro - 5 years, 4 months ago

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