Is Zero/Infinity a valid mathematical expression? What does it mean?

Answer 1

I don't think most of these answers are from math people. No expression is valid or valid without stating the context in which you are reading it. 2 + 2 = 4 is invalid if you are working in base 3.

In general, infinity is not considered a number, but is more shorthand for writing something arbitrarily big. In more traditional math your expression could be written

lim x->inf 0/x, and it equals 0. This is not really very interesting, since 0/(anything) = 0 and lim x->inf (anything)/x = 0.

There are however some areas of math that do actually use infinity or infinities in conjunction with regular numbers. In these cases 0/inf is perfectly well defined.

You have to be very careful when working with infinity. For instance, look at lim x->inf lim y->inf x/y. The inner limit is 0, since as y -> infinity it is arbitrarily small. Then the outer limit is the limit of 0, 0, 0, 0... = 0.

If you switch to evaluate the x before the y, however, you get the limit to be inf, inf, inf,... = infinity, thereby "proving" that 0 = infinity.

So, in general I would say this is not a valid equation, though there are contexts where it could be.

Answer 2

I've got the feeling youre actually asking about the fraction 0/inf yes?

Well anything over infinity tends to zero, but the real clincher here is that zero multiplied by anything = 0.

In a way it is not a valid mathematical expression because infinity is not a real number, it is only used to see what happens as you increase a value towards infinity.

A more valid way of phrasing your expression is this:

Lim (x-->inf). 0/x

This expression means we're finding the limit of the expression 0/x as we increase x to infinity.

And the answer is zero.

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Similarly you could invert the expression and ask:

Lim(x--->inf) x/0

Your answer now is *undefined* as zero is a much more powerful idea than infinity and dividing by zero will blow up your expression no matter than you are doing with the numerator.

But, good question - something to think about and often weird to get your head about.

Answer 3

Whenever you go through math, you explore that there is a necessity of identity.
Let @ be any operator & if a@b=a then b is said to be identity with respect to the operator @. @ can be adddition, Substraction,Multiplication, Divition,logarithm,power or anything else.
now you see that a+0=a & a-0=a so we can say zero is identity with respect to addition & substraction. so Zero is definitely a valid mathematical expression since it forms the pillars of math,addition & substraction.
Similarly, you see 1 is identity wrt Multiplication, Divition
I'm not too sure whether infinity is a valid mathematical expression or not, But its existance is essential. & it also forms a pillar of modern math, Integration. Infinity is more of an abstract idea. & it trully depends upon the judge (for in some cases even 10 is treated as infinity(poisson ditrn) & in some cases 10 million is not)

Answer 4

Actually u can find the answer at the dictionary. however i'll try to use my own word in this...

Zero - it means nil. when there is nothing or no numbers between [1 till (infinity minus 1)] can be used to count or value the object which basically isnt any valid object as it is Zero, which is nothing at all.

Infinity - The never ending figures. It is used when the calculation or value will never reach a specific ending or a specific figure. It is also used when a certain calculation cant reach a conclusion. For example, 1 divided by 0.

i hope that helps u well, as i myself aint that good in maths... cheers~

Answer 5

Zero is valid, but I'm not sure about infinity. Zero is the concept of nothing, and it's the number in-between positive and negative numbers. Infinty is the concept of being infinite - going on for ever, and never finishing.

Answer 6

we can say that it is a valid expression cause 0 has no value but due to that counting has formed and there are whole numbers starting from 0. thus 0 has transformed maths.

Answer 7

zero means too small to matter
infinity means too large the calculate
both are rather realtive and not absolute.
we talk of lines having '0' thickness and
limit tending to infinity.so zero and infinity are rather relativistic terms and do not have absolute value

Answer 8

zero/infinity is an undefined singularity

what may be interesting is the evaluation of f(x)/g(x) as f(x) approaches zero and g(x) approaches infinity. the answer to this depends upon the functions f and g (how "fast" does f approach zero compared to how "fast" does g approach infinity).

Answer 9

No, you can not have infinity on the bottom line of a fraction. it is null. The only time you can have this is when it is a limit approaching infinity

Answer 10

Zero is a concept that revolutionized math and created a quantum leap forward in all areas of science. The arabs gave us zero.

Infinity is the oldest math concept. Even the bible tries to express it as an attribute of their one God, El.