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.
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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
\(\displaystyle\lim_{x\rightarrow +0} \;\frac{6}{x}\;=\infty\\~\\~\\ and\\~\\ \displaystyle\lim_{x\rightarrow -0} \;\frac{6}{x}\;=-\infty\\\)