You need to move your studies on about 1800 years from the ancient Greeks to the 17th centuryAD.If you want to argue about infity vs zero, my favorite example is this;
A. For any real world number, you can subtract (or add) 1 repeatedly and it WILL reach the real world number of zero.
B. For any real world number, you can add or subtract 1 from it and it CAN NEVER reach the theoretical value of "infinity".
And I knew that would be your answer.x/x = 1
ie; "how many dogs are there in a dog". Always 1.
So what would the lawyer say? Would they pick one of the two different answers you have given, or something else entirely?The solution to ?*0 is not possible for a mathematician but is fairly easy for a realist or a lawyer.
And so you have highlighted the problems pure math has in working with infinity. No big surprises there....
The numerator and denominator are both 0 at x=2.5. So is the answer 0 because 0 times anything, including 1/0 = ?, is zero? Or is the answer 1 because anything divided by itself is 1?
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There are not two different answers to the initial question. Pure math, within its limitations gives an equal credibility to the concepts of zero and infinity, so "infinity * 0" cannot be resolved. It is "the irresistable force vs the immovable object" where both have been defined to be equally credible.... (re infinity * 0)
So what would the lawyer say? Would they pick one of the two different answers you have given, or something else entirely?
No problems at this end, I fully understand why a mathematician will think "infinity*0" is unsolvable. Can you open YOUR mind, and allow attempts at solutions that extent BEYOND math to use some of the other tools at our disposal? Math is only a subset of reality, although the arrogance of mathematicians is legendary so few will ever admit maths "dirty little made-up secrets".Studiot said:...
You have two choices,
You can listen, enquire further and learn, or you can close your mind and carry on.
Math has no problem with this problem, but I notice that you have chosen not to use your "tools outside pure math" to even attempt an answer.And so you have highlighted the problems pure math has in working with infinity. No big surprises there.
And you once again contradict yourself.The lawyer would very quickly realise zero has a very high credibility and can exist in the real world, where "infinity" is a contrived concept that very low credibility outside of the small arena of pure math. So it becomes "a low credibility irresistable force meets a high credibility immovable object" and the answer to that is the immovable object wins. infinity*0 = 0
I'm waiting for you to show us how those solutions that extend beyond math will answer the question I posed, which has a very definite finite solution that is equal to neither 1 nor 0.No problems at this end, I fully understand why a mathematician will think "infinity*0" is unsolvable. Can you open YOUR mind, and allow attempts at solutions that extent BEYOND math to use some of the other tools at our disposal? Math is only a subset of reality, although the arrogance of mathematicians is legendary so few will ever admit maths "dirty little made-up secrets".
Yes this is exactly the point, we are talking about functions (or series) not single points as with your old teacher's adageCan I just add to all this (mind I am only beginner):It is my understanding that when people write about infinity they generally write: approaches infinity. Much like they write: Approaches zero. That's why they talk about limits and not about actual values.
I like to believe my teachers old rule in this: I have zero apples in my hand no matter how far into infinity I still have to take them from the tree when I am hungry.
I'm not following. The second line is clear, but what is the basis for the first line?Can I just add to all this (mind I am only beginner):It is my understanding that when people write about infinity they generally write: approaches infinity. Much like they write: Approaches zero. That's why they talk about limits and not about actual values.
I just love the argument:
\(\frac{0}{0}=0*0\)
Where:
\(\frac{0}{0}=0*0^{-1}\)
I noted this earlier.Infinity does not have a place in all number systems.
But it's not undefined.0/0 undefined
Most people are quite relaxed with the idea that there is more than one solution toAssume 0/0 = 1
If by "philosophical" you mean trying to explain something based on what you would like to be true or what would be nice if it were true, then you have taken a step many thousands of years backward when the explanation for why objects speed up as they fall was based on equating a falling object to a weary traveller whose pace picks up the closer to home that they get and since an object's home is clearly on the ground and not in the sky, it will go faster the closer it gets to the ground.It was just my interpretation of the previous discussion and my attempt of being philosophical using math:
And this is based on your assertion that 0 times absolutely anything is 0. You then use this assertion to basically prove this assertion. Well, I could assert that 1000=12 and "prove" all kinds of things, including that 1000=12. But your only basis for this assertion is that it makes you feel good and you then choose to ignore the myriad of problems and contradictions that result if this is the case, presumably because facing those would make you feel not so good.\(\frac{0}{0}\neq 0*0\)
where
\(\frac{0}{0} = 0*0^{-1}\)
It doesn't matter from my perspective since
\(0*0 = 0\)
and thus
\(0*0^{-1} = 0\)
Which would imply:
\(\frac{0}{0}= 0*0\)
And the basis for the final line in my basic understanding would be: something times 0 remains 0.
This is absolutely a horrible example to hang your hat on. First off, you are talking about a particular set of floating point representations, all of which are fixed width. The NaN and Inf values are merely flags used to identify particular situations in which the value cannot successfully be represented within the limitations of the basic representation. But there are an infinite number of perfectly fine values that cannot be represented. For instance, in a 32-bit IEEE floating point representation, multiplying 1x10^20 by 1x10^20 will produce one Inf. But the answer is clearly 1x10^40 -- a well-defined number that is certainly not infinite.I can not multiply what is not there and how computers solve this (matlab uses NaN and Inf for possible outcomes depending on what you are doing).
My2p