You can't mix real numbers and nonreal numbers. It causes problems that cannot be explained.

You *say* that zero times infinity is zero, but can you prove this? No, because it is the "immovable object versus the unstoppable force" paradox.

What is inf(0) ? I am legitimately curious what else it could be.

Why do you guys always default to saying it is undefined/ indeterminate or something like that? There are no reasons of why it would be indeterminate. 0 times anything is 0. Anything divided by itself is 1 . These are the identity property of multiplication and the zero Property of multiplication. Why would these universal properties not apply?

You're trying way too hard to quantify infinity. It's an abstract concept.

tvrocks. anything times or plus infinite equals infinite. so when you have a number that is supposed to remain infinite regardless of what happens to it multiplied by a number that is supposed to change a number to 0 regardless of what the number is, you're left at a standstill.

How many 9s are there behind the decimal point in .9 repeating? Infinity, right? This proves that you can use infinity as a way to measure the amount of something, and that it can be used in math.

@yoyo: that depends on if you believe there to be multiple infinities. If you do the.n the idea that some infinities would be bigger than others is not weird, and it should be easy to understand that the inf +8 is a bigger infinity than the original inf, right?

@tvrocks
Which property is more important? the one regarding infinity or the one regarding 0? That's why your math doesn't work

What you guys are saying can't be said to be "using math" at all.

@yoyo: why is infinity a different situation? If the other ones are universal then they are more important.

How are you the one to determine that as mathematical truth?

tvrocks, inf +8 is not bigger than inf. I agree than there are different infinities but there is no such thing as one being bigger than the other. adding 8 to infinity implies that there is a last digit to add it to, which there is not.

but if you where to say that 999999.... and 8888888... are different infinities, that would be true, because there is a first value. however 99999... is not larger than 88888... because they each have infinite digits.

To put this in layman terms,let's say you have 888888 and 999999. Each have 6 digits and therefore 999999 is larger. However, lets look at 8888888 and 999999. the first value has more digits and therefore 8888888 is larger.

When you have infinite digits, the number of digits don't stop making 888888... and 999999... impossible to tell whether which is larger.

That still doesn't change the fact that anything times infinity is infinity.

@tr: I am not. It is a law of mathematics, and those laws are universal, just like the laws of physics.
@yoyo: if there are different infinities, but tjeu do not differ in size, then isn't there just one infinity? Please explain how there could be multiple of a set interval if they are the same. If my point is true then it would mean that, though both may be written as infinity, one of them may be written incorrectly and should be written in a way that would make it easy to distinguish between them.

You're not getting the point. they are not the same. They are do differ in size, but by an indeterminate amount. It's not possible to tell whether 999999... is larger than 888888...

let me ask you a question:
you have two numbers. You only know the first digit. 8 and 9 respectively. which is larger? That's how ridiculous your question is. what if you knew the first 2 digits? The first 100 digits? The first 10 billion digits? Are you getting it now? They are different, but that's literally all you know.

You do know that statistically speaking one of them is more likely to be bigger. That idea also doesn't apply here as you are using the same infinity in both cases. If you acknowledge that some are bigger than others, than you are also acknowledging that each of the infinities have different, though comprehensible, values. If there is an infinity, and you add 8 to an infinity to the same value, then the infinity +8 would be bigger, right?

tvrocks is a lost cause on this. some people just can't grasp abstract mathematical concepts like infinity.

he's taking infinity and making it a real number and not agreeing that inf + 1 = inf + 2 because that would have to imply that 1 = 2 when you subtract inf from both sides, even though that mathematical concept only applies to real numbers.

Infinity can be used to express the value of something, just like a number can. as such it can be used in math as it does have value, and your arguments that "it cannot be used" are false. Let the thread die if you want, I have devoted more time than I intended to it already. (It was entertaining though.)

The example is the number of 9s after the decimal point in .9 repeating, or the number of rational numbers between 1 and 2.

Here's a quick google definition of number. "a quantity or amount"

1.9 repeating is odd while 2 is even

my eyes are literally bleeding please help

https://www.google.com/webhp?sourceid=chrome-instant&rlz=1CAASUB_enUS602US602&ion=1&espv=2&ie=UTF-8#q=.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999%2F3*3

wtf you can't call something that isn't a natural number odd or even

but 1.9 repeating is natural, it is 2

That assertion was bad... 2 is divisible by 5 without a remainder while 1.999... Is not though.

why, because the way you learned to divide in fourth grade wouldn't work out too well for that numeric representation?

I guess that 2is evenly divisible by 2 while 1.999.., is not which should qualify it as even, that assertion is a stretch though.

but IT IS, just because you can't grasp the infinite concept when you envision doing out division by hand doesn't make it not divisible, get out of elementary school dude

it's all about limits, you have to appreciate limits if you want to talk about numbers represented by infinitely repeating digits.