rather than using limits, you can use simple algebra to show why you can't divide by zero.
first, take expression like 1/0 and make it into an equation.
1/0=x
this equation would be equivalent to 1=0x
0x equals zero according to the multiplicative property of zero
so you get 1=0 which is simply not the case.
but what about 0/0?
this would be equivalent to 0=0x
which then gets you 0=0
so in the equation it works, so can it be done? well, not really. the problem is we have to solve for x, so then we have to answer what is x? well, x can literally be anything because anything times zero equals zero. so you pretty much get 0/0= all real numbers, which simply can't be the case for a division operation which is why it is instead expressed as undefined.
first, take expression like 1/0 and make it into an equation.
1/0=x
this equation would be equivalent to 1=0x
0x equals zero according to the multiplicative property of zero
so you get 1=0 which is simply not the case.
but what about 0/0?
this would be equivalent to 0=0x
which then gets you 0=0
so in the equation it works, so can it be done? well, not really. the problem is we have to solve for x, so then we have to answer what is x? well, x can literally be anything because anything times zero equals zero. so you pretty much get 0/0= all real numbers, which simply can't be the case for a division operation which is why it is instead expressed as undefined.
I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them.
-Galileo
-Galileo
