Dividing by Infinity

[AV1611VET]

Is it true that n/∞ = 0?

 

[JustMeSee]

n=∞

What does that equal?

 

[Tomk80]

Is it true that n/∞ = 0?

No. It is arbitrarily close to 0, not 0. Although that statement is also incorrect.

Infinity is a concept, not a number. You cannot divide by a concept.

Dividing by infinity is shorthand for the limit of p going to inifinity for n / p. Which basically means that if you divide by successively higher numbers, the result is going to be successively closer to 0.

 

[Elendur]

Infinity needs some very cool extensions to the regular axiomatic approach.
Therefore you'll need some unique, high level math to deal with n/∞ = 0 since the real axis usually doesn't include ∞.
The interval (∞,&#8734 means that it includes all values up to, but not including, infinity.

You can let something go towards infinity, with the limit definition.

If you take lim[h->∞](n/h) then you can say it equals 0 since it'll be infinitely close to 0. The same way 0.99999... = 1.

I might have got something wrong here, I didn't reference any specific source and I'm not so well versed in the concept of infinity.

 

[JustMeSee]

Logically, I don't believe it would equal zero, unless n equals 0. But I too am not a high level mathematician.

 

[AV1611VET]

No. It is arbitrarily close to 0, not 0. Although that statement is also incorrect.

Infinity is a concept, not a number. You cannot divide by a concept.

Dividing by infinity is shorthand for the limit of p going to inifinity for n / p. Which basically means that if you divide by successively higher numbers, the result is going to be successively closer to 0.

Okay, thank you.

 

[RickG]

Is it true that n/∞ = 0?

Solving:

n = 0 (&#8734 ; anything multiplied 0 is 0.

but, what if you said n/∞ = 1 ; different story. n = 1(&#8734 or simply ∞.

BTW, what is "n"? It would be nice to know what you are dividing infinity into.

 

[AV1611VET]

Solving:

n = 0 (&#8734 ; anything multiplied 0 is 0.

but, what if you said n/∞ = 1 ; different story. n = 1(&#8734 or simply ∞.

BTW, what is "n"? It would be nice to know what you are dividing infinity into.

Doesn't n in an equation stand for "number" -- as in any number?

 

[RickG]

Doesn't n in an equation stand for "number" -- as in any number?

Yes, but that number stands for something. What is n, a distance, temperature, time, rate, etc..

Also, infinity cannot be zero by definition. Infinity is an unbound limit, therefore it has a value. Simply put infinity always increases or decreases without bounds.

Having said that, there is an exception when describing a one dimensional Riemann surface. That is a really interesting area of mathematics (geometry) but also gets pretty complicated.

May I ask what the point of the OP is?

 

[Lethe]

No. It is arbitrarily close to 0, not 0. Although that statement is also incorrect.

Infinity is a concept, not a number. You cannot divide by a concept.

Dividing by infinity is shorthand for the limit of p going to inifinity for n / p. Which basically means that if you divide by successively higher numbers, the result is going to be successively closer to 0.

Taking your last statement to be the case, that infinity is shorthand for the limit of p going to infinity for n/p, there are at least two proofs I can think of to demonstrate the equivalency of lim_p->inf of n/p and 0.

They are equal.

 

[Lethe]

Hmm.... I'm thinking of the proof of 0.9 repeating being equal to one.

0.9 repeating to the nth decimal place is equivalent to 1-1/(10^n)

0.9 repeating is equivalent to the limit n -> inf of (1 - 1/ (10^n) ).

and there are two proofs I can think of showing that 0.9 repeating are equivalent to one.

Therefore 1 = 1 - lim (1 / (10^n) ) => lim 1/ (10^n) = 0

And since 10^n is a monotonic sequence, there's a 1:1 mapping from n to 10^n.

Isn't that about right?

 

[AV1611VET]

Yes, but that number stands for something. What is n, a distance, temperature, time, rate, etc..

Also, infinity cannot be zero by definition. Infinity is an unbound limit, therefore it has a value. Simply put infinity always increases or decreases without bounds.

Having said that, there is an exception when describing a one dimensional Riemann surface. That is a really interesting area of mathematics (geometry) but also gets pretty complicated.

May I ask what the point of the OP is?

I happened to run across this:

For those that have not worked with infinite number sets,

2 x (infinity) = infinity
AND
(any number)/(infinity) = 0.

... and was curious.

QV the OP in that thread as well.

 

[quilbilly]

That was fun. New question

How many angels can sit on the head of a pin?