The most counterintuitive result ever!!!!

[DarkBlack]

Steve, a lot of physics solutions involve infinity, usually as a limit in a calculus equation. QUOTE]


Hmm... How can there be a limit when dealing with infinity?

 

[DarkBlack]

Yes, except for the assumption that 1-1+1-1+1-1+1-... = 0.5 or 1/2. "Because we don't know whether to stop after a +1 or after a -1, we just average the two possible answers," is just a completely arbitrary solution. .

Just as arbitrary, in my humble opinion was to start with a +1, then a -1. If they started with a -1 first the finite addition would have tallied between -1 an 0, as apposed to +1 and 0.

 

[Loren49]

Steve, a lot of physics solutions involve infinity, usually as a limit in a calculus equation. QUOTE]


Hmm... How can there be a limit when dealing with infinity?

Just a little explanation of limits:
Limit (mathematics) - Wikipedia, the free encyclopedia

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.[1] Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.

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Check out the two examples at the referenced site....one approaches infinity and the other approaches 2. Neither ever gets there but does get as close as you want. For example the one that approaches 2 can be shown was 1.9999999... with the 9 repeating as many times as you'd like.

Mathematics can be very interesting and useful.

Loren

 

[DarkBlack]

I was having a little fun with a play on words. You know the common sense idea of "limit" contradicting the common sense idea of infinity.

 

[jaotguy]

a mathematician , an engineer and a regular joe were given a task ... at the end of a room was a glass of beer ... they were told they could only move 1/2 the distance remaining per move and had to reach the other end of the room ... both the engineer and the mathematician threw up their hands and said it wasn't possible. ... the regular person said he thought he could get close enough to solve the problem.... sometimes "close" is good enough.

 

[xtn]

Just as arbitrary, in my humble opinion was to start with a +1, then a -1. If they started with a -1 first the finite addition would have tallied between -1 an 0, as apposed to +1 and 0.

Sure, but you are inadvertently falling into the same trap. There is no "finite tally" to an infinitely long equation. Okay I should rephrase that. Sure, you can quit calculating the equation anywhere you want and come up with some finite tally, but it is arbitrary and doesn't have anything to do with the infinitely long equation any more.

xtn