Let the number you say, anything, be x.
Now let's test the properties of division (by zero)
Property 1: (for x ≠ 0)
\(\frac{x}{0} = ∞\)
Property 2: (for x ≠ 0)
\(\frac{0}{x} = 0\)
Property 3: (for x ≠ 0)
\(\frac{x}{x} = 1\)
However, when x = 0 in all properties,
\(\frac{0}{0}\) could be infinity (property 1), 0 (property 2), or 1 (property 3).
But, this equation does not make sense, since you cannot share nothing to nobody.
Therefore, there is no solution to \(\frac{0}{0}\)
Therefore, dividing by zero does NOT make sense at all.
from MathWizard2004 A.K.A. MathW0122
Let the number you say, anything, be x.
Now let's test the properties of division (by zero)
Property 1: (for x ≠ 0)
\(\frac{x}{0} = ∞\)
Property 2: (for x ≠ 0)
\(\frac{0}{x} = 0\)
Property 3: (for x ≠ 0)
\(\frac{x}{x} = 1\)
However, when x = 0 in all properties,
\(\frac{0}{0}\) could be infinity (property 1), 0 (property 2), or 1 (property 3).
But, this equation does not make sense, since you cannot share nothing to nobody.
Therefore, there is no solution to \(\frac{0}{0}\)
Therefore, dividing by zero does NOT make sense at all.
from MathWizard2004 A.K.A. MathW0122
I'd like another mathematician to confirm what I have written here please.
MWizzard has asked me to comment on his answer. (I hope I got your gender right MWizzard )
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You have said that x/0 is infintiy but what if is negative then that could not be right.
Basically you simply cannot divide by zero - it is always undefined.
What you can say is :
Find the limit of 6/x where is is positive but as x tends to 0 then the answer would be +infinity
you would write it like this
\(\displaystyle\lim_{x\rightarrow +0} \;\frac{6}{x}\;=\infty\\~\\~\\ and\\~\\ \displaystyle\lim_{x\rightarrow -0} \;\frac{6}{x}\;=-\infty\\\)