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If you integrate two infinities

two infinities which canceled each other out

The idea of infinity is a sophisticated one and it is very often bandied about with a great lack of understanding.

But, as to having infinities of 'different sizes': Imagine adding a series of numbers together1+2+3+4+5 +++++ and keep going as long as you wanted, and a bit longer - 'for ever'. That would give you what we would call 'infinity'.Then you added up the squares of the numbers:1+4+9+16+25 ++++++ and keep going for the same length of time.The second total would always be bigger than the first total.

Both totals would be 'infinity', if you keep on for ever but the second total would always be a lot more than the first total.

So there you have the idea of infinities of different sizes.There are many cases where you can 'compare infinities' which are, on their own, incomprehensible, but the ratio of the two can have a meaning.Infinity is definitely not for the squeamish or the unwary but lots of my whacky Mathematician friends get very excited about it.

ifninities

There is not a coherent 'English' description of Infinity -

You have to go to Maths for a safe way to define it

One increases faster than the other

so, however far you go, it is always bigger.

There are times, however, when you can use infinity more safely. For instance, if you add up the series of numbers1+1/2+1/4 + 1/8 +++ you will never get a total more than 2 - even for an infinite number of terms. We can use the word 'infinite' safely because the final result is finite. That is a 'convergent' series, as opposed to a 'divergent' series like the first two examples.

Studying what happens 'on the way' to infinity can give you a clue about what would happen if you just carried on and on. . . .

It's just too hard for a simple definition and you can't expect one any more than you can put Relativity or Quantum Mechanics in simple terms.

I think I have heard this used before to make people think they are inferior.

There is no 'value' for infinity. How could there be if it is the result of a process which has no limit?

As a school boy I tried to argue that zero times infinity was one from the arithmetical statement 1/0 equals infinity and 0/1 equals zero therefor 1/0 * 0/1 the zeros cancel out and one is left with 1/1 which equals one.My argument fell on deaf ears !

So, the possible amount of stars, molecules, atoms, quarks.We're looking up through the eye of infinity doing our best to count our way out:)

True:)But who will count it down if finite.An approximation will have to do.But that's not the number.So what we reach for, even if finite, will never be counted.

yet there is another absolute of mathematics that that breaks. 0 times anything should be 0, so why wouldn't 0 times infinity be 0?*calling all mathematicians*

There is no 'value' for infinity.