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Infinity

by Zac
(Syracuse, NY)











































On your website it states that any number divided by zero is infinity, hence why your calculator cannot do it. This is incorrect. y/x = infinity, when y is any real number and x is approaching zero. Consider this:

20 / 0 = x

This, by definition implies that:

0 * x = 20

Which is a problem!

Comments for Infinity

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Jan 25, 2010
Dividing by Zero
by: Staff

The problem


On your website it states that any number divided by zero is infinity, hence why your calculator cannot do it. This is incorrect. y/x = infinity, when y is any real number and x is approaching zero. Consider this:

20 / 0 = x

This, by definition implies that:

0 * x = 20

Which is a problem!


The solution


1. This type of apparent contradiction is interesting and fun. A mathematical proof which shows that contradictions are equally true is called a paradox.

There are hundreds of math paradoxes. For example, there is a simple proof which shows that 1 = 2, or that 0 = 1.

Common sense tells you such a paradox cannot be true, yet the algebra appears to prove that it is true.


2. To understand what is happening, it is important to remember the algebra used must begin with a premise which is true. Algebra cannot be based on a fallacy.

20 / 0 = x is not true, 20 / 0 is not a valid algebraic expression.

20 / 0 = undefined (I prefer infinity, but Zac is technically correct: y/x = infinity, when y is any real number and x is approaching zero.)


The problem stops at this point. 20 / 0 is not a valid algebraic expression. No further computations are possible.


3. It is worth noting that while division by zero is undefined in the real number system, it is possible to divide by zero in other number systems.


Staff
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