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# what is infinity divided by (infinity - 1)?

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4799
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what is infinity divided by (infinity - 1)?

Mar 4, 2015

#5
+8

Infinity doesn't behave like an ordinary number, and shouldn't be considered as an ordinary number.

Some infinities are bigger than other infinities, in fact one infinity can be infinitely larger than another infinity. Infinity/infinity or even infinity/(infinity - 1) is an indeterminate quantity and can be equal to anything between zero and infinity, without further information you just don't know, that's why it's called indeterminate.

Mar 5, 2015

#1
+272
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THIS IS NOT A PROPER ANSWER: this may or may not be about number theory, and that may or may not be a topic we cover on this calculator forum. but i like it so imma see what i can do

$${\frac{{\mathtt{\infty}}}{\left({\mathtt{\infty}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}} = {\frac{\infty}{{\mathtt{\,-\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}\infty}}$$

thanks calculator.

lets see, an infinite value divided by one less than that infinite value.

well, as numerator value goes up (1/1, 2/1, 3/1) value goes up.

and as denominator goes down (1/3, 1/2, 1/1) value goes up also.

$${\frac{{\mathtt{\infty}}}{\left({\mathtt{\infty}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$ would follow the same pattern as 5/4, 4/3, 3/2, 2/1, and 1/0 (which is interesting also because 1/0 is sometimes considered to be infinity)

by heading into the equation calculator and entering$${\mathtt{x}} = {\frac{{\mathtt{y}}}{\left({\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}}$$ and$${\mathtt{y}} = {\mathtt{1}}$$

and then repeatedly adding 1s to y every time i see what the result is, i have concluded that the bigger y is, the closer y/(y-1 gets to being 1. for example, 2/1 = 2

but then 3/2 = 1.5,
4/3=1/333...
5/4=1.25

and eventually i just put 1+1+111111111111111 or something and got 1.00000000006

so yeah it just heads toward zero. so infinity/infinity-1 would be either 1 or 1.000000... and an infinite string of zeroes followed by a single one.

but what do i know

Mar 4, 2015
#2
+22015
+8

∞ - 1 is still infinity; so you have  ∞/∞.

But this is an indeterminate value; that is, it could have many different answers; the answer depends upon the question from which it arose --- it could be ∞, or -6, or 1, or π, or ... depending upon the problem.

Just pay attention when you take calculus ...

Mar 5, 2015
#3
+272
0

yeah but wouldnt that be like saying x/(x-1) = x/x = 1, which makes x=all? 3/(3-1) ≠ 1? i dont have any more points about that i just wanted to make sure it was noticed (because its important)

while your point still stands because its infinity and stuff, i would like the mention one more thing

infinity/infinity is not indeterminate, its definetely 1. any number divided by itself equals 1, and while we may not be able to say what value infinity holds it is definetely equal to itself (reflexive property).

infinty is just an interesting topic ok?

Mar 5, 2015
#4
+112861
+8

Infinity is not a number TJM

You can not think of it like an ordinary number - it does not work that way.

Mar 5, 2015
#5
+8

Infinity doesn't behave like an ordinary number, and shouldn't be considered as an ordinary number.

Some infinities are bigger than other infinities, in fact one infinity can be infinitely larger than another infinity. Infinity/infinity or even infinity/(infinity - 1) is an indeterminate quantity and can be equal to anything between zero and infinity, without further information you just don't know, that's why it's called indeterminate.

Guest Mar 5, 2015
#6
+272
+5

oh ok but does infinity/infinity = 1 because for every value in infinity there is an identical one to match?

nobodys going to see this because its too far back but im asking anyway.

also is that what cardinal numbers are? i tried reading the wiki page on them but it wasnt very easy to read.

im really done this time i wont ask any more infinity questions ( for now )

Mar 6, 2015
#7
+112861
+5

No TJM,

infinity /infinity is  undefined.

The Cardinal number of something is how many individual elements it contains.

so it has to be 0 or a natural number, that is 0,1,2,3 etc

So if you are talking about all the days of the week then the cardinal number is 7

I  am not sure if I am using my parts of speach correctly.

You usually talk about cardinal numbers in relation to sets.

The cardinal number of a set is how many elements it contains.

See TJM i did see your post.  It would be extremely rare for me to not see a post!

Mar 7, 2015