Discussion Forum Unit 2
Discuss how the limit allows a way to “divide by 0”.
The question of division by 0 has never been a difficult one, although there might be issues to arise
with it. It is said that the division by 0 is possible if the result is determined. To do so we need to
expand the algebra.
I think that serious doubts start to arise after studying rational numbers, when for any number x,
except 0, is introduced the concept of the inverse 1/x and hyperbola graph: y(x) = 1/x
graph
It is obvious that when dividing 1 to very small number we get large numbers, and the less is x, the
more becomes 1/x. So why can’t we say that 1/x=∞ is a certain number?
The algebraic objection to this is as follows: Suppose that ∞=1/x is a number. Then all the rules
that
exist for ordinary numbers should apply to this number. In particular, on one side the relation
0*
∞ = 1 must be true, and on the other side, since 0 = 1 − 1, 0
*
∞ = 1
*
∞ − 1
*
∞ = 0. Thus, we get
1 = 0, and therefore follows that all numbers are equal to each other and are equal to zero. Indeed,
since 1 * x = x is true for any number x, then 1
*
x = 0
*
x = 0.
At this point, you probably ask yourself: “Well, isn't that complete nonsense?”
Of course, this is complete nonsense, if we are talking about ordinary numbers. However, I
emphasized the word “rules
” above for specific reasons.