Odd fraction includes pi and infinity

[firelavarock]

does pi over infinity equal .00000...314159...?

if not please post opinions. :(

 

[gb7nash]

If you're only allowing real numbers, this operation is not allowed. If you're dealing with the extended real numbers, then pi/inf = 0. In fact, any real number over infinity is 0.

 

[micromass]

Hi firelavarock!

It seems that you have some misconception about mathematics here:

does pi over infinity equal .00000...314159...?

First, infinity is not a number. Thus dividing through infinity is not possible and makes no sense. The question "what is 2/infinity" is the same thing as "what is 2/apple". Infinity and apple are not numbers and we can not calculate with them.

Secondly, if you write 0.00000... then the zeroes go on forever, it doesn't stop. So asking what the last digit of 0.000... is, is meaningless. There is no last digit.
Equivalently, 0.0000...314159... is meaningless, the sequence of 0's will go on forever, and there is simply no place to start with 314159...

 

[firelavarock]

oh I thought that it was just above 3 infinitesimal

 

[berkeman]

oh I thought that it was just above 3 infinitesimal

Could you please explain what you mean by that? And where did you get the information for your first post above (where did that equation come from?). I'm about ready to call troll...

 

[micromass]

oh I thought that it was just above 3 infinitesimal

There are no infinitesimals in (standard) mathematics. And even if you would define infinitesimals, then they wouldn't have decimal representations...

 

[firelavarock]

I read that an infinitesimal is a decimal point followed by an infinite number of zeros and then a one. So I thought that that 3.14... infinitesimals might be a decimal point followed by an infinite number of zeros followed by 314... .

Can you more clearly explain what I did wrong? Thanks.

 

[micromass]

I read that an infinitesimal is a decimal point followed by an infinite number of zeros and then a one.

I don't know where you read that, but that is wrong.

 

[berkeman]

I read that an infinitesimal is a decimal point followed by an infinite number of zeros and then a one. So I thought that that 3.14... infinitesimals might be a decimal point followed by an infinite number of zeros followed by 314... .

Can you more clearly explain what I did wrong? Thanks.

Please provide attribution for your original post (OP). Where did you read this, or did you just make it up?

 

[Mentallic]

I read that an infinitesimal is a decimal point followed by an infinite number of zeros and then a one.

Obviously you are having trouble with the notion of infinite. An infinite string of zeroes means that the zeroes never end. So you can't ever put a 1 at the end... An infinitesimal is just like infinite, they're not numbers, they're concepts.

 

[firelavarock]

in physics forums what is 1 over infinity I saw several posts that had infinitesimal as the answer.

so if pi is just above three. isn't it just above 3 over infinity?
or am I looking at it all the wrong way?

1/infinity=infinitesimal

you were right about this, an infinitesimal is an infinite number of zeros after the decimal point with a one at the end, but of course there is no end but ah well!

infinitesimals are very interesting, archemedes used them to find the volume of the sphere, Newton also used them to work out velocity and related stuff.

now days it is used to explain bronwian motion and other nasty topics.

This is what I mean.

 

[Mentallic]

in physics forums what is 1 over infinity I saw several posts that had infinitesimal as the answer.

They would be using the extended real number line, which isn't the conventional system that most of us use.

so if pi is just above three. isn't it just above 3 over infinity?

That would be what you didn't see. If you saw 1 over infinite being referred to as an infinitesimal rather than zero, then you wouldn't be seeing 3 over infinite being an infinitesimal times 3. Again, an infinitesimal is just a concept.

or am I looking at it all the wrong way?

Yep.

edit: Just as the poster mentioned in your quote, an infinitesimal is an infinite string of zeroes followed by a 1. But when does infinite finish? It doesn't. "Putting the 1 at the end" is just a way of trying to say that the number is not 0 in the extended real number line. You could put any number you wish - a 2, 9, 10, or even pi - but this doesn't mean anything since you won't be putting that number there anyway. In other words, it's still an infinitesimal and it means that 1/infinite is no different to 2/infinite or pi/infinite.
But anyway, in all cases that you'll be dealing with, it's equal to zero.

 

[micromass]

I consider that post by steppenwolf to be entirely wrong. 1/infinity is not defined for real numbers. You may define it using the extended number line, but then 1/infinity =0, not some kind of (non-zero) infinitesimal.

Furthermore, saying that infinitesimals are an infinity of 0's and then a 1 is completely incorrect.

 

[Redbelly98]

... an infinitesimal is an infinite number of zeros after the decimal point with a one at the end, but of course there is no end but ah well!

This is what I mean.

steppenwolf's statement contradicts itself -- if there is no end then there is no "one at the end". If you can't see that, then it's unlikely you can understand many of the explanations being given here and this whole discussion is pointless. I'm seeing zero progress towards understanding any of the replies here.

Thread locked.