# Second highest and lowest numbers

#### iooqxpooi

##### Member
Second highest and lowest numbers

The second highest number is:

99.9(with the bar over the last nine)% x infinity

The second lowest number is:
infinity - [99.9(with the bar over the final nine)% x infinity]

#### TimeWizardCosmo

##### Senior Member
Zenith
Second highest and lowest numbers

What? There can't be a 2nd highest or second lowest number -- Maybe a second highest percent, but not a second highest number.

#### Jean-Jacques Mass

##### New Member
Second highest and lowest numbers

Due to the nature of infinity even the highest conceivable number is infinitely far away. There is no "infinity - 1", unfortunately - what interesting equations we could make if it were so!

#### The_Ruffneck

##### Member
Second highest and lowest numbers

infinity x anything other than 0 is still infinity , infinity % by anything is still infinity , you got some crazy ideas...

#### iooqxpooi

##### Member
Second highest and lowest numbers

I know, it is flawed...hehehe.

I edited it to equal-

Second:

Smallest number=infinity^-(infinity^(infinity^(infinity^(infinity etc.

Highest number=infinity^(infinity^(infinity etc.

#### Alpha and 0mega

##### Junior Member
Re: Second highest and lowest numbers

Hey iggy,r u sure u r 13?

#### Harte

##### Senior Member
Re: Second highest and lowest numbers

<div class='quotetop'>QUOTE(\"iooqxpooi\")</div>
The second highest number is:

99.9(with the bar over the last nine)% x infinity

The second lowest number is:
infinity - [99.9(with the bar over the final nine)% x infinity]

[/b]

I miss ol'e Iggy. Always had some good stuff in his posts. He got this one wrong, as he said subsequently. He got it wrong in that post too, though it appeared he was just playing around anyway.
I know a simple way to express infinity minus one though:

lim(x->o) [1/x-1]=inf.-1

Harte

#### fanavans

##### Junior Member
Re: Second highest and lowest numbers

There are CLASSES of infinity.

Consider this question - are there more even numbers then counting numbers? The answer is no, there are the same amount of each, an Infinite amount.

Are there the same amount of counting numbers (integers) as there are numbers? No.

Here's why:

Consider a group(set) on numbers representing the counting numbers:

{1, 2, 3, 4, 5, 6, ...Infinity}

Consider a set of numbers representing the even numbers

{2, 4, 6, 8, 10, ...Infinity}

Now there are the same amount in each set. You can see that by putting them above eachother: Vis

{1, 2, 3, 4, 5, 6, ...Infinity}
{2, 4, 6, 8, 10, 12, ...Infinity}

They map out. No matter how many you add (or count) in each set, there are still the same amount.

But that doesn't happen when you include irrational numbers. You can map out the numbers between 1 and 2 against infinity, and the numbers between 2 and three against infinity etc. So you have a bigger infinity as it were. (this is all kosher maths, I can't remember the blokes name who came up with it).

Anyways, I'm not sure what the point is - oh hang on - Which infinity-1 are we talking about? Well, either that or trying to show off the only thing I remember from an advanced maths course...

#### Harte

##### Senior Member
Re: Second highest and lowest numbers

<div class='quotetop'>QUOTE(\"fanavans\")</div>
There are CLASSES of infinity.

Consider this question - are there more even numbers then counting numbers? The answer is no, there are the same amount of each, an Infinite amount.

Are there the same amount of counting numbers (integers) as there are numbers? No.

Here's why:

Consider a group(set) on numbers representing the counting numbers:

{1, 2, 3, 4, 5, 6, ...Infinity}

Consider a set of numbers representing the even numbers

{2, 4, 6, 8, 10, ...Infinity}

Now there are the same amount in each set. You can see that by putting them above eachother: Vis

{1, 2, 3, 4, 5, 6, ...Infinity}
{2, 4, 6, 8, 10, 12, ...Infinity}

They map out. No matter how many you add (or count) in each set, there are still the same amount.

But that doesn't happen when you include irrational numbers. You can map out the numbers between 1 and 2 against infinity, and the numbers between 2 and three against infinity etc. So you have a bigger infinity as it were. (this is all kosher maths, I can't remember the blokes name who came up with it).

Anyways, I'm not sure what the point is - oh hang on - Which infinity-1 are we talking about? Well, either that or trying to show off the only thing I remember from an advanced maths course...[/b]

Good catch Fanavans. There is also no such number as "infinity minus one." My formula above approaches infinity as x approaches zero.

Your memory serves well as far as the "classes" of infinity goes. As I recall, these are called "cardinal" infinities and I believe they number four.

Your argument about irrational numbers is slightly incorrect though. There are more irrational numbers between zero and one than there are rational numbers on the number line. A rational number is a number that be expressed as a ratio, you probably know. So the number "2" can be represented as 2/1, this set also contains all the fractions you can write (3/4, 88/89, etc.) They are still outnumbered by the irrational numbers, even the ones between zero and one.

I know a fairly straightforward way to envision this fact, I'll post it later if anyone is interested.

Harte

#### Keroscene

##### Active Member
Re: Second highest and lowest numbers

This reminds me of something I heard once and was wondering if an awnser was actually possible.

If the temperature is zero degrees out today, and it will be twice as cold tommorrow, what will the temperature be?