I.e. The set of natural numbers N(1,2,3,...100,101,...10000000,...n, n+1) is infinite, however, the set of real numbers R has more numbers (a larger infinity) between 1 and 2 than all numbers in set N.
I can prove this by showing I can always find a new number that couldn't be listed between 1 and 2 1.a(1)a(2)a(3)a(4)...a(100)...etc 1.b(1)b(2)b(3)b(4)...b(100)...etc 1.c(1)c(2)c(3)c(4)...c(100)...etc
What is our new number that would never appear on this list? 1.a(1)b(2)c(3)
You're welcome, brainlet
Lucas Sanders
FPWP
Samuel Lewis
Also, decimal numbers are a different kind of infinity. Think infinitisimal, not infinity. They're different. The number is extremely close, but never reaches it because we can always list a new decimal within the 3 to 4 interval.
Carter Rodriguez
wouldn't the set of quaternion matrices be the largest infinity?
Hunter Roberts
No
Noah King
3 is also infinite in extension, you can write it as 3.000... with an infinite number of 0's after it.
Also, if that blows your mind, you will SHIT a LUNG when you read about transcendental numbers...
Gabriel Cruz
Lol. The real numbers aren't the largest infinity, just larger than the naturals.
Kevin Green
π can equal 3 or equal 4 or any number in between, depending on how you measure
but π is always a number greater than 3 and less than 4
Joseph Thompson
4.00000000000000000000...
Tyler Hernandez
The real numbers are uncountable, and thus the largest infinity, dickturd. You can only differentiate between uncountable and countable when it comes to infinity.
Nicholas Johnson
No, that image makes no sense. There is a certain point that occurs very early on when you cannot remove small boxes from the perimeter.
Levi Lewis
>the power set of X is strictly larger than X >[math] 2^\mathfrak{c} > \mathfrak{c} [/math]
this is literally elementary set theory why are undergrads invading Veeky Forums
Joseph Turner
Big statement there boy. Prove to me that there exists no bijection between the reals and its powerset.
Julian Perry
Math is funny, huh? Get this >0.99repeating (that is an infinite number of 9s in the decimal expansion) is equal to 1. Not rounded up to 1 but exactly equal to 1. Observe. "Bar" represents infinite repetition since I have no key to represent it. >0.99bar = 0.33bar • 3 >0.99bar = 1/3 • 3 >0.99bar = 1
James Brown
you arrived at an untrue statement, aka a contradiction
Eli Long
It is no more Real than 2 or 4. Nowhere in nature is there anything that is 2 units or 4 units. Everything breaks down to 3d energy waves that cannot be placed specifically so no distance can be measured, only approximated.
Pi is NOTHING MORE than a ratio for the improbable. Approximation.
x^2 + y^2 = 1 breaks down at the smallest unit. There is no value when x and y = the smallest unit possible because a smaller unit would be required. It is all fuzzy illogic.
in the natural number can you find a number between 1 and 2? 1=2 q.e.d.
Austin Stewart
Because geometric series converge and every real number has a decimal representation which must be bounded by a geometric series.
Jose Butler
...
Jack Long
1/∞
Colton Scott
Its because numbers are a language, and all languages have limitations. It can be smaller because every proceeding number represents an ever smaller fraction of the whole. Same barrier you encounter when halfing indefinitely. Ulitmatly between every whole number the is an infinite number of fractions or decimal places.
Sebastian Davis
Because 3.14... < 4.14...
Liam Sanchez
>Infinity exists in a concept >but people still argue materialism
