infinite numbers

So you see, there are two infinities: one of integers and one of real numbers. The latter is larger than the former, even though there is an infinite number of integers keep counting and eventually you'll get to any. This is not so with reals, because there are an infinite number of real numbers in a single integer you can never progress past one. We don’t know any infinite ``numbers'' yet, but we can see that some infinite ``number'' must exist in order to describe the number of elements in the set of real numbers. So we decide to just give this infinite ``number'' a name. We call it ℵ<sub>0</sub>. We call this symbol ℵ<sub>0</sub> ``aleph-null.'' Aleph is just the first letter in the Hebrew alphabet, and null just refers to the 0 subscript. ℵ₀ is not a number in the way that 5 or 12 million or 3.79384509 is a number. We cannot count ℵ₀ out on our fingers, we need to just become comfortable with the idea that ℵ0 is simply DEFINED to be the cardinality of the natural numbers, which is a certain infinite "number". Because ℵ0 is infinite, it is very large, so large that we cannot write it down except to write ℵ₀

>so large that we cannot write it down
pfft, aleph null(integer limit) is smaller than (1/0) "real infinity"
((1/0)/0) infinity divided by zero is even bigger
(division by zero is eq multiplication by infinity)
((1/0)^(1/0)/0) (inf^inf)/0
(((1/0)^((1/0)^(1/0)))^(1/0)^((1/0)^(1/0))))/0

The universe is finite, its matter is countable. Wake up from your dream.

>>2

(1/0) "real infinity"

Nice shitpost.

>>1
It's pretty yucky really, there both essentially 1D, and dividing integers by some very large aleph-0 makes them equal the reals

The simplest proof would be that there is no two real numbers that are both not greater and not less than each other without being equal

but we can see that some finite ``slope'' must exist in order to describe the rate of increase in the set of "real" values. So we decide to just give this finite ``slope'' a name.

Using slope 1/inf >0 makes the set uncountable but it is still essentially integer-ordered

>>8
assuming integer infinity(aleph-null) 1/(aleph-null)=0.000...1,
but infinity can be in domain of reals as well.

>>7
Who are you quoting?

>>10
My dubs.

It's the same as if you partition the integers into an infinite number of fractions, won't each partition still have infinitely many integers?

if inf/2 = inf, inf/inf = inf?

>>13
Inf isn't NaN, inf/inf should technically be 1, but different(e.g. limit) values of inf make it undefined.

>>14
Infinity is not a number, so no it wouldn't be 1.

put the first million in partition 1 to 1000000
second million goes in 1 to 2000000 stride 2
ad infinitum

What programming language is this?

>>17
Lambda Calculus

As width 1000000 tends toward inf, minimum members per partition -> inf

* er, maximum members

How is infinity larger than another infinity?

>>21
Different process to reach them. An example with fictional banks and money.
Like if you had 2 banks each started with 100$ account of different percents rates.
Now imagine one bank gives you +110% daily but another multiplies your money x1000.
They both can reach "infinite money" but if we compare them by yearly rate,
the progress is much faster on the second bank.
At any point in time, the second bank account will be much larger than first.

>>4,8
https://en.wikipedia.org/wiki/Infinite_set

>>22
a bad example

>>24
Infinite set comparisons operate on the same principle.
https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument#Uncountable_set

>>2
Wrong

Usary is wrong and shall be forbidden under the Sharia.

Canada's Criminal Code limits the interest rate to 60% per year.
In japan the limit is 20% per year, bar pawnshops.
Each U.S. state has its own statute which dictates how much interest can be charged before it is considered usurious or unlawful.

It would be better to set the maximum interest over the life of the term to 10-15% and be done with it

>>27
Sharia banks still do usury, sorry

Infinite niggers.

>>30
African Americans*

>>30
tsk.

dubs