Who is this "Khan"?
"You’ve managed to kill just about everyone else, but, like a poor marksman, you keep missing the target."
Who is this "Khan"?
Hi Capt, Lakon.
Yes, you two have highlighted the illogic of dividing zero by any non-zero number. It is basically a 'non-starter' contrived situation, and not a serious action/process in any sense or system.
@Lakon
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With regard to the apple story.
When there is no apple to divide, and it is theoretically divided among zero pupils, the result is still no apple.
Yet mathematically, some people believe that zero divided by zero equals one.
That you get an apple from nowhere.
Possibly but zero divided by zero is ONE. Binary computing simply does not have the capablility to perform such an equation, unless anyone has a different algorithmn to describe binary mathematics. *looks about*...
$$5^0=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$
And just what does $$1-1=?$$
"You’ve managed to kill just about everyone else, but, like a poor marksman, you keep missing the target."
Undefined: Since this thread keeps growing despite the fact that it was answered decisively on page 1, I finally went ahead and read your position. You seem to be claiming that we should treat zero as fundamentally different from other real numbers, more like a state of balance than a number. Is that fair? If so, then how could we use zero in math? Would you have to come up with a whole different set of rules describing how to do math with zero as opposed to doing math with other numbers? I'd be very curious to hear what those rules might be.
Please don't misunderstand me. I have no argument against that stage or 'functions' per se. I only want to explore what is the reality treatment at its most fundamental levels in BOTH cases: ie, where zero is treated in any 'functions' context; and where zero is treated in any 'number' context.
I already have presented my own more fundamental arguments that zero is NOT a 'number' OR a 'function' of any kind. But rather it is a state or condition or symbol for origin etc etc invoking physical aspects such as 'superposition' and 'trivial action' effectively a NON-action (as I pointed out to rpenner that his separation of the zeros in "0/0" expression is trivial and not proper in view of the "Rules of evaluation of expressions" is properly invoked and maintained throughout for ANY "like/like" expression, including zero/zero if that ever arises).
So I am not pursuing the set theory stage/function arguments, just the most fundamental illogics which arise per se if/whenever zero is in reality context trivially/invalidly being attempted to be treated as 'a number' or manipulated trivially 'functionally' as I already pointed out to rpenner.
Please do carry on with your own set/function approach to your discussion with the OP et al. I have no argument with you so far, mate!
You are trying to defining your own mathematics without any valid definition.
In set theory, 0 has a precise definition.
$$\emptyset=\{x:x\neq x\}$$
and then zero is defined as
$$0\equiv\emptyset$$
How then would you render in mathematics the reality of a zero dimensional void being reflected in a mirror(s)?Quantum Quack: I think you're going about the problem backwards. If we have a mirror reflecting nothing, then that's a physical arrangement of objects, and it is what it is. It makes no sense to ask "whether the reflected zero is the same as the original zero" because the universe doesn't care about number systems; it just does physics, and we use number systems to describe and predict its behavior. Now if you put some units on the zeros, they might describe some property of the real system, in which case we could do math with them and get meaningful answers.
Can I throw a can or worms at ya all???
say we have a table with a mirror.
On the table we have nothing and in the mirror we have a reflection of nothing.
So now we have zero plus a reflected zero,.
Questions:
1] By using a mirror have we just divided or multiplied the zero in to two zero's (0 = 0*2)
2] Can one say they are the same zero?
3] Does either zero, the source or reflection, still equal zero?
using a vertical line as a mirror symbol we could have the notation 0|0
(0|0) / 0 = ?
Seriously curious...
Extended:
Say we have two perfectly parallel mirrors and place zero [nothing] in between, do we essentially have an infinite number of reflected "unique" zeros or only one zero?
OK $$5^0=\frac{5^1}{5}=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$
Sorry, that would be more conventional. Clearly though, what you posted is different from what I posted. Are you following any convention? Could I construe that $$5^5=\frac{5^5}{5^5}=1$$ from your post just as easily?
And when I say that you are not of the opinion that zero is a natural number, it's OK really. Hint! Hint!
But Good luck with your Theory of Everything from scratch!
and ($$5^5=\frac{5^5}{5^5}$$)
Your other expression/construct expansion $$5^5=\frac{5^5}{5^5}=1$$ creates an INVALID extension