# QuestionWhy is there no symbol for "not possible" in Mathematics?

#### IG2007

##### "Don't criticize what you can't understand..."
Actually, my question is more large. The thing that made me think this is division by zero. Any positive number or negative number or zero itself cannot be divided by zero. Rather say, no integer can be divided by zero. And that is what gives the answer as infinity. And this is the thing that has gave rise to theories of blackholes which have 0 volume and as Density = Mass/Volume, the density of the blackhole becomes infinite.

My question is related to this but not fully. Any number multiplied by zero is zero. So, zero multiplied by infinity is also zero and there is no higher value than infinity in mathematics. Okay, 0/0 is infinity, this is alright. But, what about 1/0 or 2/0 or 100/0... These numbers will never come in the table of zero, and thus logically it is not possible to divide 100 by 0.

My question is, there is a symbol for infinity, i.e., But, there is no symbol for "not possible", why? No positive or negative number can be divided by 0, so why isn't there a special symbol for that? And, I believe, it is this confusion that has led to the theories of blackholes, which say that blackholes have "infinite density"?

#### akashrao

okay, let us approach it from the other side - if there were a symbol let us say # for 'not possible' then how would you use it - can you gimme an expression for instance using this symbol?

• IG2007

#### IG2007

##### "Don't criticize what you can't understand..."
okay, let us approach it from the other side - if there were a symbol let us say # for 'not possible' then how would you use it - can you gimme an expression for instance using this symbol?
I would use it for things like, 100/0, -1/0, 99999/0 or rather say, division by zero.

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#### akashrao

okay

'100/0 is not possible' is the expression you wanted to say i believe ...

then perhaps if we wrote 100/0 = # it would mean that the value we get by dividing 100 by 0 is impossible to define ...

however, impossibility pertains to the feasibility of happening of something - whether a mathematical operation is either possible or not possible!

symbols are usually used to denote mathematical operations, and quantities and as qualifiers ... possibility or impossibility is a question of logic so it comes under that - mathematical logic ...

so i could come this far ... could you take it further?

• Catastrophe

Moderator

#### akashrao

right, maths is indeed fun when i was learning imaginary numbers i used to see stars at college so imaginary number is not possible but the concept has multiple uses ... as i was taught back then ...

#### IG2007

##### "Don't criticize what you can't understand..."
I study in class 7 only and haven't yet read of imaginary numbers.

My simple logic for making an imaginary number that is equal to not possible is: the greatest possible value in Mathematics is infinite. And I infinity x 0 is 0 and there is no positive or negative number in the whole table of 0 until infinity. So, 100/0 is not possible because we cannot get an answer except 0 in the infinite table of 0. We need a symbol for that to represent it.

#### akashrao

right, you would get a better hold of the idea of infinity as you grow up for the moment, think like this - division of a number by 0 is mathematically impossible, and we do not get any result out of it which we can quantify - it can not be counted, so we place an undefined figure there called infinity in the place of the result; therefore it being immaterial whether we divide by 0 a -ve number or a +ve number, however small or big, irrespective of signs, we get the same undefined value of infinity however, mathematics does not say that division by 0 is not possible; mathematics simply says what we get for now is infinity ...

and you know why we get infinity when we divide by 0? you would be learning it in higher mathematics - well it is something like this:

when in a fraction x/y where x is constant, let us say y = 10, you get x/y = x/10 = some a; now let us say y = 5, you get x/y = x/5 = some b where b > a (you can put some value for x and check this) ...

now let us say y = 2, you get x/y = x/2 = some c where c > b > a; now put y = 1, you get x/y = x/1 = some d (which is equal to x) where d > c > b > ...

now put y = 0.5 you get x/y = x/0.5 = some e, where e > d > c > ...
now put y = 0.2 you get x/y = x/0.2 = some f, where f > e > d > ...
now put y = 0.1 you get x/y = x/0.1 = some g, where g > f > e > ...

now put y = 0.05 you get x/y = x/0.05 = some h, where h > g > f > ...
now put y = 0.02 you get x/y = x/0.02 = some i, where i > h > g > ...
... (and the argument continues ...)

as you therefore experimentally notice, in the fraction x/y as we decrease y, the value of the fraction is increasing, i.e. x/y as a result is higher as y is lower in the denominator; in calculus which you will learn soon we re-phrase this like - x/y tends to be higher than ever before as y tends to be lower than ever before a value; putting some math terminology in, we now have

x/y tends to be higher than ever before as y tends to be 0, the least possible positive number available but not positive

as y goes low x/y goes high as you can plot a graph of x/y against y
as if y becomes 0 i.e. so low, x/y goes so high as if we can not comprehend how high, so to say we don't have so much of a graph sheet available to plot that value there

so this very high value of x/y as y tends to 0 (written y->0) is now un-plottable or so big as to be un-reachable to mathematical perception which is therefore given a new term infinity since this very high x/y can not be defined or plotted on graph when y = 0 therefore y can never actually be = 0 but can only tend to 0 i.e. y->0

therefore as y = 0 is not feasible we said division by 0 is not possible since it yields so high an imperceptible a value to our intellect that we can not plot it on graph sheet mathematically, we write it as x/y -> ~ as y -> 0 (sorry ~ is the only symbol i got on my lappy to mean infinity for now )

so that's it #### IG2007

##### "Don't criticize what you can't understand..."
Sir akashrao,

I just tried to plot a graph of x value = 0 and y value = 0 and I went back to where I started. The origin is the point 0. I agree that 0/0 is infinity because infinity times 0 is infinity. But, if you say, 1/0 = infinity, I disagree. Because, that doesn't make any sense. If infinity x 0 = 0, then how come 1/0 = infinity? How come infinity x 0 = 1? That is the reason we need the symbol "not possible".

#### akashrao

infinity is something on which mathematical operations, when performed, yield abrupt results which are unbelievable ... it is an abstract idea of a large, immensely large quantity only • IG2007

#### IG2007

##### "Don't criticize what you can't understand..."
That is what I am trying to change. By the way, I just got to know now, that infinity x 0 is not equal to 0. But still, the logic is still the same. 1/0 is not possible, so is not any thing else.

Moderator
Why are people so caught up on trying to do math on infinity? You can't add to it, subtract from it, multiply or divide by it. You can approach it, by continually dividing by smaller and smaller numbers, but you can never reach it.

-Wolf sends

#### akashrao

right, understood ...
so instead of saying 1/0 = infinity you just wanna say that 1/0 is an impossibility if i am not wrong ...
in doing which therefore ending up not with some undefined quantity called infinity but rounding off logic right by saying that division by 0 is not possible ... !

however, mathematics is a highly creative subject ... believe me, when you begin dealing with differential and integral calculi then this infinity becomes indispensable an idea there ... so to just begin with giving a rudimentary idea about this infinity it is now being introduced at this level by writing out, 1/0 is infinity ... 2/0 is infinity ... 3/0 is infinity ...

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
right, you would get a better hold of the idea of infinity as you grow up for the moment, think like this - division of a number by 0 is mathematically impossible, and we do not get any result out of it which we can quantify - it can not be counted, so we place an undefined figure there called infinity in the place of the result; therefore it being immaterial whether we divide by 0 a -ve number or a +ve number, however small or big, irrespective of signs, we get the same undefined value of infinity however, mathematics does not say that division by 0 is not possible; mathematics simply says what we get for now is infinity ...

and you know why we get infinity when we divide by 0? you would be learning it in higher mathematics - well it is something like this:

when in a fraction x/y where x is constant, let us say y = 10, you get x/y = x/10 = some a; now let us say y = 5, you get x/y = x/5 = some b where b > a (you can put some value for x and check this) ...

now let us say y = 2, you get x/y = x/2 = some c where c > b > a; now put y = 1, you get x/y = x/1 = some d (which is equal to x) where d > c > b > ...

now put y = 0.5 you get x/y = x/0.5 = some e, where e > d > c > ...
now put y = 0.2 you get x/y = x/0.2 = some f, where f > e > d > ...
now put y = 0.1 you get x/y = x/0.1 = some g, where g > f > e > ...

now put y = 0.05 you get x/y = x/0.05 = some h, where h > g > f > ...
now put y = 0.02 you get x/y = x/0.02 = some i, where i > h > g > ...
... (and the argument continues ...)

as you therefore experimentally notice, in the fraction x/y as we decrease y, the value of the fraction is increasing, i.e. x/y as a result is higher as y is lower in the denominator; in calculus which you will learn soon we re-phrase this like - x/y tends to be higher than ever before as y tends to be lower than ever before a value; putting some math terminology in, we now have

x/y tends to be higher than ever before as y tends to be 0, the least possible positive number available but not positive

as y goes low x/y goes high as you can plot a graph of x/y against y
as if y becomes 0 i.e. so low, x/y goes so high as if we can not comprehend how high, so to say we don't have so much of a graph sheet available to plot that value there

so this very high value of x/y as y tends to 0 (written y->0) is now un-plottable or so big as to be un-reachable to mathematical perception which is therefore given a new term infinity since this very high x/y can not be defined or plotted on graph when y = 0 therefore y can never actually be = 0 but can only tend to 0 i.e. y->0

therefore as y = 0 is not feasible we said division by 0 is not possible since it yields so high an imperceptible a value to our intellect that we can not plot it on graph sheet mathematically, we write it as x/y -> ~ as y -> 0 (sorry ~ is the only symbol i got on my lappy to mean infinity for now )

so that's it "right, you would get a better hold of the idea of infinity as you grow up "
"Why are people so caught up on trying to do math on infinity?"
Cat • IG2007

I remember.

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
Why is there no symbol for "not possible" in Mathematics?

Unless I have missed it, why has no one given the answer?

Hint: There are two in this post.

Cat • IG2007 and COLGeek

#### IG2007

##### "Don't criticize what you can't understand..."
I guess I know what you mean to say Cat, no one has given the answer. And "not possible" is not possible in Mathematics.

I don't think that "not possible" is not possible in Mathematics, Cat. I think that it is rather necessary.

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
Sometimes a little checking up is useful before jumping in:
https://en.wikipedia.org/wiki/Question_mark
The question mark "?" (also known as interrogation point, query, or eroteme in journalism) is a punctuation mark that indicates an interrogative clause or phrase in many languages. The question mark is not used for indirect questions. The question mark glyph is also often used in place of missing or unknown data.
Something unknown is also not possible (to know). Plus, minus, multiply and divide are normal parts of English as well as being used in mathematics.

#### IG2007

##### "Don't criticize what you can't understand..."
As far as I have studied Maths (that's very less compared to you all), I have come to know that in Statistics, there is a thing called "variate" which gives the value to a variable, that's the literal meaning of the word. So, not everything that's unknown is impossible to know. Except future and division by zero.

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
As far as I have studied Maths (that's very less compared to you all), I have come to know that in Statistics, there is a thing called "variate" which gives the value to a variable, that's the literal meaning of the word. So, not everything that's unknown is impossible to know. Except future and division by zero.
[/QUOTE

Something unknown is also not possible (to know). Plus, minus, multiply and divide are normal parts of English as well as being used in mathematics.

I did not say that all words use in maths had common English meanings. Be careful not to argue from the particular to the general. Reptiles are animals. Monkeys are animals, therefore monkeys are reptiles.

Multiply is a mathematical term.. Variate is a mathematical term. Therefore multiply and variate are both mathematical words. This does not allow for the fact that multiply has other meanings which are not mathematical terms.

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