Does anyone else believe that 1 over 0 = infinity?

Question

For me it is not undefined.

I know the limit as x approaches 0 of 1/x equals infinity. But that means that zero is a finite number.

Answer 1

That is a very theoretical question that mathmaticians don't like to hear.
Zero was just recently added to math. Before it wasnt even a number. It was only an idea.
Think about it this way,
What happenes when you zoom in to the size of a proton? Now a needle point seems like infinity to you.
What about the size of a string( if you believe in string theory)? Now an electron seems infinitely big.
Infinity and zero are so relative to the observer that they must be related.
The problem with this relationship is that it breaks down mathematics to only an observation and not an absolute truth. Every mathmetician thinks that math is the universal language, and no mathematician or physicist for that matter wants to even ponder the possibility that everything they have dedicated their life for could have flaws.
So as an everyday person 1/0 is just undefined.
But to anyone who wants to think past our rules of math and see ideas zero is just as indefinite as infinity.

Answer 2

1/0 is in fact undefined in the real number system, for two reasons:

First, division is usually defined to be the inverse of multiplication. For 1/0 to have any value, it would be necessary for there to be some x such that x*0=1. However, x*0=0 for all real x, and so 1/0 cannot be assigned a value.

The second reason is that if we try to add a value to the real number which, when multiplied by 0, equals 1, (i.e. if we try to use the same trick we pulled with √(-1) to create the complex numbers), we end up breaking our number system. Let us define v*0=1. Then:

1 = v*0 = v*(0+0) = v*0 + v*0 = 1 + 1 = 2

Oops, there goes the distributive property.

1 = v*0 = v*(0*0) = (v*0)*0 = 1*0 = 0

Oops, there goes the associative property as well.

v² = 1/0 * 1/0 = 1/0 = v
v²-v=0
v(v-1)=0
v=0 or 1?

Well, okay, that one's just a little stupid, considering that two sentences ago I told you the distributive property doesn't work on v, and then used it anyway to compute the factorization. But you see my point -- any solution, infinite or otherwise, that satisfies v*0=1, will quite rapidly proceed to break all laws of mathematics and common sense. It is for this reason that 1/0 is always left undefined in elementary arithmetic.

That said, is is possible to construct supersets of the reals in which 1/0 does have a solution, which is denoted ∞ (see, for instance, the real projective line), but in these number systems ∞*0 is left undefined, and division ceases to be simply the inverse of multiplication. Note that this is an unsigned ∞, not +∞ or -∞. It is impossible to assign 1/0 to a signed infinity while still preserving limits (e.g. [x→0+]lim 1/x = ∞, but [x→0-]lim 1/x = -∞, so if 1/0 were defined, it would be inconsistent with at least one of these limits). As such, 1/0 is still undefined on the extended real line.

Edited to add:
"I know the limit as x approaches 0 of 1/x equals infinity. But that means that zero is a finite number."

Actually, [x→0]lim 1/x is not defined (as I previously mentioned, the left-hand and right-hand limits are different. But the main thing I wanted to note is that zero IS a finite number. Where did you get the idea that it isn't?

Answer 3

It has lot of significance in modeling and developing concepts.
On a different note , however, in relative terms if it not undefined for you then either it is really undefined for all... or....it is well defined and you are :)
Thirdly... how many times you can take out 0 from 1.Count please.....
Fourthly....think of 1/x and keep increasing x such that 1/x becomes so small that it is meaningless or useless ...... then x would become infinite....you can think in terms of time, space, or other quantity.
on the fifth note, mathematicians are still note able to assign a quantifiable number for this term.
On sixth, we are able to give a number to 1, 2 ,3 -4,-10 etc. but not the infinity.Basically all these numbers are just a concept...some....or most ..( again a relative term..;) ...) of them are defined nd others are not.
on seventh ,I would say that we may be dealing with larger number in future when we develop more science.
You may have noticed that a few thousand years back our numbers were very small......slowly... we are knowing more terms for larger numbers.
It is basically 0/0 which does not have an answer... again... how many times 0(nothing) can be taken out of 0(nothing)

I am sure by now this has become very long... going towards infinity.

Answer 4

I don't.

Let's assume you're speaking the truth. Then 1/0= inf. Multiplying by zero, 1 = 0*inf. As zero times anything is zero, then 1=0, which is false. But if not, then at least multiply by (say) 2, and get 2 = 2*0*inf., or 2 = 0*inf., because 2*0 = 0. Thus 1=2.

Whaddya think?

Answer 5

it is undefined.
but limit of 1 over something converging to 0 is infinity.

Answer 6

i'm an atheist so via definition, i don't have self belief in any God. Calling absolute countless set "god" could sound cool to a mathematician yet i elect testable info formerly i think, not in basic terms some attractive math allegorical syllogisms.

Answer 7

it is undefined, because if you divide 1 over 0, you will get an undefined answer. that is why it is undefined.