Little math theory question

I was saying that if you can divide by zero, then all numbers are equivalent.
 
No. If you could divide by zero, all numbers would be zero. In fact I proved that in this thread. Obviously it means they're all equivalent (because they're equal).
 
newfangle said:
No. If you could divide by zero, all numbers would be zero. In fact I proved that in this thread. Obviously it means they're all equivalent (because they're equal).
Wouldn't they also all be one?
 
In other words they are all equivalent. If all numbers are equivalent to zero then they are all equivalent as well.
 
Bluemofia said:
In other words they are all equivalent. If all numbers are equivalent to zero then they are all equivalent as well.
Exactly, you're initial idea sucked becase it was comprehensible to the average forum member.
 
Tomoyo said:
What is infinity/(infinity^2)? It should be 1/infinity, zero, but I think it can also be 1.

Or can infinity not be squared?
It depends what's infinite and what's the square of infinity.

If there are an infinite number of people that have ever and will ever live, and you want to know the ratio of that to the ratio of seconds in all of eternity squared, the answer will not necessarily be 1 or 0; it could be anything. That's why maths sucks.
 
Before I hand off my thoughts in a hopefully more clear and simple manner, I want to say special thanks to Cantor, who introduced "Aleph" into math (the "a" of Hebrew) :goodjob:

The simple rules are that aleph (of any rank) times aleph (of any rank) equals aleph (of the highest rank from them 2).

Since power is more precedented than division,
Aleph_N / (Aleph_N^2) = Aleph_N / Aleph_N = 1.

I'm happy hope you're happy 2.
 
newfangle said:
So you're saying math sucks because it can't deal with the qotient of two numbers that aren't defined?
I'm saying it sucks because it tries to deal with them, even though they are meaningless. If maths was more clever, it wouldn't need us to tell it whether a result has meaning or not, it would just do it. Like imaginary numbers attempts (and succeeds) to add meaning to the root of a negative number, but there's no such thing with infinity.
 
Mise said:
I'm saying it sucks because it tries to deal with them, even though they are meaningless. If maths was more clever, it wouldn't need us to tell it whether a result has meaning or not, it would just do it. Like imaginary numbers attempts (and succeeds) to add meaning to the root of a negative number, but there's no such thing with infinity.

Well, math is based on reality, and if there is no meaning in reality, then no calculation should come to this point.
"imaginary" numbers exist since they ARE defined well as a field, like normal numbers are, and thus have a meaning and can be reached to solve real life problems.
 
i know what you mean with imaginary numbers, but i disagree with what you're saying about maths being based in reality. Physics should be the ...uhh... "real" part of maths, and maths should be purely abstract, IMO, so that Maths can deal with things like infinities and 0/0 's without resorting to a physical interpretation.
 
Mise said:
i know what you mean with imaginary numbers, but i disagree with what you're saying about maths being based in reality. Physics should be the ...uhh... "real" part of maths, and maths should be purely abstract, IMO, so that Maths can deal with things like infinities and 0/0 's without resorting to a physical interpretation.

Yes, but even in math you can only handle things that are defined -
multiplication is correctly defined for the Z3 = {0,1,2} group for example, but not for the Z4 = {0,1,2,3} group, because 4 is not prime and thus the group is not a field. (2*3=2=2*1 ==> 3=1 , contradiction).
Math only handles well defined things and phisics use it.
 
To paraphrase some great mathematician, every concept developed in Pure Mathematics is eventually used in practice.

Consider the Quaternions. For those unknowing, the quaternions are a 4th dimensional extension of the imaginary numbers. They are also one of the only non-commutative fields in existence.

Low and behold a hundred years after their discovery, a little bloke named Einstein comes along and forwards this crazy idea of a 4-th dimensioonal universe. Crazy!
 
newfangle said:
To paraphrase some great mathematician, every concept developed in Pure Mathematics is eventually used in practice.
In the 1850s, an English mathematician named George Boole invented Boolean Algebra as a means to mathematically express certain logical operations. Almost a century later, his Algebra was being used to design electronic signal circuits and computers.
 
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