Sythe Users: What Do They Know? Do They Know Things?? Lets Find Out! #5

[Accounts Shop]

Walter, jim's brother from another mother, is facing execution by death for being friend with jim.

His overlords are giving him a chance to redeem himself if he can prove without a doubt to his overlords that there are more real numbers than there are natural numbers

Being a little bit retarded, Walter has come to you in hopes that you might be able to save him and his family of people!

Quick, to your drawing board!

to save Walter, you must come up with a mathematically correct proof that the size or R > the size of N

Any valid mathematical proofs can be used to solve the problem

Free Walter!

#ObamaCare

 

[Thatnameistaken]

To bad Walter is just a musician like the rest of the Shitty people, and does not know much math or phsyics. Luckily, by banging his head against the rocket hard enough, Walter has deduced the bloodflow from his head to his toes is = the square root of -1, there for proving aliens aren't yellow.

 

[Accounts Shop]

To bad Walter is just a musician like the rest of the Shitty people, and does not know much math or phsyics. Luckily, by banging his head against the rocket hard enough, Walter has deduced the bloodflow from his head to his toes is = the square root of -1, there for proving aliens aren't yellow.

by doing so, walter merely found the irrational number 'i'

 

[Thatnameistaken]

And by having found I, knowing it is a real number but not a natural number, walter has pleased said overlords.

 

[Accounts Shop]

And by having found I, knowing it is a real number but not a natural number, walter has pleased said overlords.

that is not how it works, the overlords are not pleased with your attitude young boy

 

by doing so, walter merely found the irrational number 'i'

It's not really correct to talk about a non-real number as rational or irrational. i is complex.

Walter, jim's brother from another mother, is facing execution by death for being friend with jim.

His overlords are giving him a chance to redeem himself if he can prove without a doubt to his overlords that there are more real numbers than there are natural numbers

Being a little bit retarded, Walter has come to you in hopes that you might be able to save him and his family of people!

Quick, to your drawing board!

Free Walter!

#ObamaCare

1. The set of all reals includes the set of all integers.
2. The set of all integers includes a subset called the set of naturals which are only non-negative integers.
3. The set of reals therefore includes includes both the set of naturals and the set of all negated naturals. Therefore it must be at least twice as large less one. Therefore it is larger.

QED

 

[Accounts Shop]

It's not really correct to talk about a non-real number as rational or irrational. i is complex.



1. The set of all reals includes the set of all integers.
2. The set of all integers includes a subset called the set of naturals which are only non-negative integers.
3. The set of reals therefore includes includes both the set of naturals and the set of all negated naturals. Therefore it must be at least twice as large less one. Therefore it is larger.

QED

But both the real numbers and the set of natural numbers are infinite set ... (2 * &#8734 is still ∞.

how can you prove that one 'infinite' is larger than the other 'infinite'?

Your logic works when working with 2 finite sets but doesn't work with infinite sets

Walter is starting to feel the heat

 

[Hamouze]

But both the real numbers and the set of natural numbers are infinite set ... 2 * infinite is still infinite.

how can you prove that one 'infinite' is larger than the other 'infinite'?

You just answered your own question by stating it is inherently flawed/unanswerable.

 

But both the real numbers and the set of natural numbers are infinite set ... (2 * &#8734 is still ∞.

how can you prove that one 'infinite' is larger than the other 'infinite'?

Walter is starting to feel the heat

The syllogism I presented remains true irrespective of the number of elements in the set, provided the number of elements is two or greater.

For example if you allow 2 elements in your set of naturals then it is {0, 1};
Therefore the set of integers is {-1, 0, 1}. If the set of reals at least must contain the set of integers then {-1, 0, 1} is a subset of the reals and therefore the reals must contain more elements than the naturals.

This works for any number of naturals >= 2, even if you take the limit to infinity (as in the case of the true set of naturals.)

E.g. n=4 it would be count({0, 1, 2, 3}) < count({-3, -2, -1, 0, 1, 2, 3})

 

[Austintheman]

by doing so, walter merely found the irrational number 'i'

xdddddddddddddddddddddddddddddddddddddddddddddddddddddddd

 

[Accounts Shop]

The syllogism I presented remains true irrespective of the number of elements in the set, provided the number of elements is two or greater.

For example if you allow 2 elements in your set of naturals then it is {0, 1};
Therefore the set of integers is {-1, 0, 1}. If the set of reals at least must contain the set of integers then {-1, 0, 1} is a subset of the reals and therefore the reals must contain more elements than the naturals.

This works for any number of naturals >= 2, even if you take the limit to infinity (as in the case of the true set of naturals.)

E.g. n=4 it would be count({0, 1, 2, 3}) < count({-3, -2, -1, 0, 1, 2, 3})

you can't use finite examples to prove the size of infinite sets

to save Walter, you must come up with a mathematically correct proof that the size or R > the size of N

time is running out!

 

[Accounts Shop]

You just answered your own question by stating it is inherently flawed/unanswerable.

No I did not, i just showed that Walter can't solve this problem with that logic, but didn't say there was no mathematically correct solutions to this problem

 

[Accounts Shop]

i'll give you some help:

if you assume that the size of 'N' is countable, how could you go about to prove that 'R' is of bigger size

 

you can't use finite examples to prove the size of infinite sets

Lol it's called a proof by induction. And obviously yes you can.

to save Walter, you must come up with a mathematically correct proof that the size or R > the size of N

time is running out!

That's not what you've written at the start.

Proof by induction is actually not even necessary. By definition naturals are a subset of integers which by definition are a subset of reals. It's very straight forward to prove these sets are not identical. Therefore they are strict subsets. Therefore each must contain at least one more element than its subset.

 

[Lilmj27]

Lol it's called a proof by induction. And obviously yes you can.



That's not what you've written at the start.

Proof by induction is actually not even necessary. By definition naturals are a subset of integers which by definition are a subset of reals. It's very straight forward to prove these sets are not identical. Therefore they are strict subsets. Therefore each must contain at least one more element than its subset.

fucken newfags amirite?

 

[Accounts Shop]

By definition naturals are a subset of integers which by definition are a subset of reals. It's very straight forward to prove these sets are not identical. Therefore they are strict subsets. Therefore each must contain at least one more element than its subset.

what you're induction proof tells the overlords is that 'N' != "R" and that 'N' would reach infinity 'faster' than 'R' but it doesn't prove that 'N' is of lesser size than 'R'.

You're induction proof also takes for granted that 'Z' has more elements in it than 'N', which it does not.

which is why you can't just use the finite set theory and apply it directly to infinite set theory

The overlords are starting to set-up the guillotine

 

The overlords believe in creationism, therefore they have no knowledge of the relationship between naturals and real numbers, therefore you can't just assume that one is a subset of another.


what you're induction proof tells the overlords is that 'N' would reach "infinity" 'faster' than "R" , but it doesn't prove that 'N' is of lesser size than 'R'


The overlords are starting to set-up the guillotine

You need definitions before something can be proved or disproved via reasoning either formal or informal.

For example if the reals is defined as potato and the naturals are defined as tomato then one is not a subset of another, they are not even sets but rather dinner.

 

[Accounts Shop]

You need definitions before something can be proved or disproved via reasoning either formal or informal.

For example if the reals is defined as potato and the naturals are defined as tomato then one is not a subset of another, they are not even sets but rather dinner.

granted, i edited my post, to include the fact that you're proof sits on the theory that the size of 'Z' > the size of 'N' but in fact, the size of 'Z' <= the size of 'N'

you have to come up with a mathematical proof that shows that |R| > |N|

 

granted, i edited my post, to include the fact that you're proof sits on the theory that the size of 'Z' > the size of 'N' but in fact, the size of 'Z' <= the size of 'N'

you have to come up with a mathematical proof that shows that |R| > |N|

Can't until you provide set definitions. You've rejected existing definitions so you need to provide your own.

 

R+1 > N+1