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Originally posted by PhysicsAdept
reply to post by MeesterB
Exactly, I get that. When I talked about Euler's formula I pointed that out, but I am asking what would happen if we did. Not to use it as a number, to but pretend that an infinite amount of diving had occurred... Open your mind to that possibility... then, what is the answer? Would you not then look at the limit? The limit is saying, indirectly, that at x=∞, 1/x=0
Originally posted by PhysicsAdept
reply to post by PhysicsAdept
The thing about this calculation is that in order to produce that result of 1/3... we assume we have reached infinity, have we not?
Originally posted by PhysicsAdept
reply to post by Bob Sholtz
Well that is certainly an interesting aspect. Who is to say that zero is defined though? Zero has a type of numerical value that shows us that it is possible to have the opposite of ∞. I don't think that zero can exist without infinity honestly...
Originally posted by PhysicsAdept
reply to post by OccamAssassin
Uhm, I don't know exactly what you are getting at, could you explain? I mean 3 in base three is merely 10, correct? I don't know how decimals work in other bases, but would it be.10r?
is possible to have the opposite of ∞.
If I divide one chocolate bar between an infinite amount of people, everyone gets nothing. So where does the chocolate bar go ?
The very sentence "1/infinity = 0" has no meaning. Why? Because "infinity" is a concept, NOT a number. It is a concept that means "limitlessness." As such, it cannot be used with any mathematical operators.
The symbols of +, -, x, and / are arithmetic operators, and we can only use them for numbers.
To write 1/infinity and mean "1 divided by infinity" doesn't make any sense. 1 cannot be divided by a concept. It can only be divided by a number.
In math, when you hear people say things like "1 over infinity is zero" what they are usually referring to is something called a limit. They are just using a kind of shorthand, however.
They do NOT mean that 1 can actually be divided by infinity. Instead, they mean that, if you divide 1 by successively higher numbers, the result becomes closer and closer to 0. If I divide 1 by a very large number, like a billion, then I get one-billionth, which is a VERY small number, but it isn't 0.
Since there is no largest number, I can always divide 1 by a bigger number. But that will just produce an even smaller number, right? It will NEVER produce 0, no matter how high I go.
Since the answer to the division is getting closer to and closer to 0, we say that "the limit of the expression is Zero." But we have still not divided anything by infinity, since that isn't a number.
You are perfectly correct in saying that "1/infinity = infinitesimally small."
But only if you realize that you REALLY mean "1 divided by a REALLY big number is a REALLY small number."