To infinity and beyond

Mathematician Eugenia Cheng has written a popular, amusing, and fascinating book on the concept of infinity.

Beyond Infinity:  An Expedition to the Outer Limits of Mathematics takes up its paradoxes, mathematical conundrums, and important uses.

For example, one mathematical axiom is that:

infinity X infinity = infinity.

But if you work out this equation by dividing both sides by infinity, you get:

infinity = 1

Since that can’t be, infinity must not be a number, exactly.  But what is it?

Read an excerpt from her book, taken from Science Friday. [Read more…]

The God of multiple infinities

There are an infinite number of numbers.  But there are also an infinite number of numbers between any two numbers!  In fact, there are more numbers between numbers than there are countable numbers, even though both are infinite!  (Mind blown yet?)  George Cantor, the father of Set Theory and a devout Christian, proved that.  Joel Bezaire shows what the concept of “multiple infinities” can do to our sense of the infinity of God. [Read more…]

Weird math fact

A comic strip  (which you can see here after the jump) raised a mathematical conundrum that I’ve been trying to get my mind around.  Maybe you can help.

(1) 9 x 1/9 = 1.   Right?  That’s what the fraction 1/9 means.

(2)  1/9 = .1111111. . .  If you turn 1/9 into its decimal form, by dividing 9 into 1, the result is .1111111. . . [meaning a repetition into infinity]

(3)  9 x (.1111111. . .) = 1    Substitute the decimal form for  1/9 in equation (1).

(4)  .9999999. . . = 1      Do the calculation in equation (3).   9 x .111111. . .  is .999999. . ., another repetition into infinity.  The number by itself is short of 1, infinitely short, but you could go into infinity and it would never be 1.  AND YET, in the equation, .99999 in an infinite regress EQUALS 1.

How can that be? [Read more…]