Hello, I just wonder about one thing: I saw that a company stopped spending a single penny in maintenance for what it was selling, so obviously it was selling less than before but they were still selling a bit, thus the "money gained"/"money invested" ratio was not just like 1000/0.00001 which would be already a big number, but basically 1000/0, and while dividing by 0 isn't possible, the story I'm telling basically still mean that the ratio should sort of be equal to "more than infinite" since when I say that they didn't spend a single penny, I really mean that it's not 1000/0+ but really 1000/0, so I just wonder, is there a name or symbol for this situation that replace the words "more than infinite" ?
Is there a "more than infinite" notation ?
- Thread starter rex4
- Start date
So, let's say kids play lottery, one bet 1$ and gain 10$, he says "I won 10 time what I bet", the other one doesn't have to bet anything and win 10$, would it be correct to say "I won an infinity more times what I bet" ? It sounds wrong since as I said, he didn't bet 1/infinity but actually exactly 0.
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,084
We sometimes informally say that [MATH]1/\infty = 0[/MATH], really meaning that the limit as x goes to infinity of 1/x is zero (that is, 1 divided by a very large number is a number very close to zero). Really, there is no such thing as 1/infinity, as infinity is not a number you can operate on; but you know that.
So you could informally say "I won infinity times what I bet", but a mathematician would be inwardly cringing.
On the other hand, what you initially said, that a ratio 1000/0 is more than infinite, is nonsense. It simply is infinite (speaking informally again: "sort of equal", as you rightly said) -- in the sense that no finite number times 0 can be 1000.
And, of course, the whole concept is really meaningless, taken literally.
So you could informally say "I won infinity times what I bet", but a mathematician would be inwardly cringing.
On the other hand, what you initially said, that a ratio 1000/0 is more than infinite, is nonsense. It simply is infinite (speaking informally again: "sort of equal", as you rightly said) -- in the sense that no finite number times 0 can be 1000.
And, of course, the whole concept is really meaningless, taken literally.
D
Deleted member 4993
Guest
If you do a google search for - "types of infinite" - you will see the following (among others):
"There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets. The theory of infinite sets was developed in the late nineteenth century by the brilliant mathematician Georg Cantor."
and:
"there must be multiple levels of infinity — the natural numbers and the real numbers are both infinite sets, but the reals form a set that is vastly larger than the naturals — they represent some "higher level" of infinity."
But unless you want to get a Ph.D. in "number theory" - you should not worry about these.............
D
Deleted member 4993
Guest
I seem to remember - reading in "One, Two, Three, .... infinity" by Gammow - that the third kind of infinity involves "no. of possible arcs" in space. I read ions ago and I don't have the book for reference so cannot totally vouch for it.
topsquark
Senior Member
- Joined
- Aug 27, 2012
- Messages
- 2,269
The continuum hypothesis does not have to do with the number of infinities. It has to do with whether the continuum is the second smallest in the class of infinities. See
Continuum hypothesis - Wikipedia
That same article indicates that the class of infinities is unlimited.
Otis
Elite Member
- Joined
- Apr 22, 2015
- Messages
- 4,414
∞+1
LCKurtz
Full Member
- Joined
- May 3, 2019
- Messages
- 475
The cardinality of the set of functions from [MATH]\mathcal{R}[/MATH] to [MATH]\mathcal{R}[/MATH].
Last edited:
