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/sci/ - Science & Math

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11750563 No.11750563[DELETED]  [Reply] [Original]

>NOOOOO ∞ IS THE SAME AS ∞+1 EVEN THOUGH THE LATTER IS OBVIOUSLY GREATER NOOOOOO

>> No.11750567

>>11750563
Infinity, as in all of the integers or reals, is absolutely unchanged by plus 1.

>> No.11750572

>>11750563
It's okay anon, we all struggle with math sometimes.

>> No.11750611

>doesn't know about infinitesimal calc

>> No.11750654

1 is a number and infinity is a concept. Numbers are concepts too but infinity is a different kind of concept. ∞+1 is like saying antidisestablishmentarianism + photosynthesis.

>> No.11750663

>>11750563
[math]\omega + 1[/math] is greater than [math]\omega[/math] though.

>> No.11750701

>>11750654
There are different sizes of infinity. For example, the number of even numbers is infinite and the number of whole numbers are infinite, yet since the number of even numbers is contained within the number of whole numbers, it must be smaller than the infinite number of whole numbers.

>> No.11750719

>>11750701
>natural numbers are infinite
>natural numbers plus 1/2 is infinite+1
>infinity+1 > infinity

>> No.11750834

>>11750719
Correct

>> No.11750898

>>11750563
The later is not greater
I'm really getting sick of fucking dumbfucks shitting up the board.

>> No.11751706

>>11750563
>OBVIOUSLY
I would say ∞ is obviously the same as ∞+1

>> No.11751736

>>11750563
order =/= greatness
they're all >R

>> No.11751741

>>11750701
bijection between them exists --> same size

>> No.11751748
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11751748

>>11750701

>> No.11751902

>>11750563
>using infinity as an integer

>> No.11752230

>>11750701
[math] f: \mathbb{Z} \rightarrow 2\mathbb{Z} [/math]
[math]x \mapsto 2x[/math]
is 1-1 and onto (trivially)
So both sets have the same number of elements

>> No.11752252

>>11750563
All numbers are the identity element for (inf, +)

>> No.11752259

>>11751741
>bijection between them exists
No, this is where you're wrong.

>> No.11752260

>>11752259
a bijection between integers and even integers doesn't exist ?

>> No.11752261

>>11752230
don't try to be smart because you will never be. sorry.

>> No.11752265

>>11752260
how are there so many highschoolers in this thread? Have none of you taken analysis?

A set is infinite if A is equivalent to one of its proper subsets. It's literally one of the first things you read in ch.2 of rudin.

>> No.11752270

>>11750701
>>11752259
>>11752261
10/10 made me reply

>> No.11752272

>>11752265
are you >>11752259 ?

>> No.11752277

>>11751736
*ordinality =/= cardinality

>> No.11752295

you are
retard

>> No.11753094

>>11750563
∞ is a concept, not a number, faggot, kys your shelve

>> No.11753140

>>11750701
>number of even numbers is contained in within the number of whole numbers
Is 5 contained in 8? You faggot cannot even articulate what you mean.

>> No.11753172

Addition is like adding a stick to another stick. Adding to infinity is like trying to add a stick to a ray

>> No.11753181

>>11750563
Define infinity + 1

>> No.11753213

>>11753094
>∞ is a concept, not a number
then it's useless. come back when it can be treated like a number.

>> No.11753222
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11753222

>>11753181
First, define infinity, which is well-defined on the extended real number line.
If infinity-1 is positive, then what's infinity+1?

1-infinity.

>> No.11753231

>>11750563
That's like saying "myself including my arm is greater than the whole of myself". You're describing the same thing in different terms.

>> No.11753377

>>11753213
it can. google extended number line

>> No.11753392

>>11753213
Infinity is not useless you fail high school math class?

>> No.11753457

>>11750567
countable infinty + 1 is a new ordinal; it has the same cardinality, however.

>> No.11753462
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11753462

>comparing infinities
Why do mathfags do this? It defeats the fucking purpose

>> No.11753475

>>11753462
This is a Tibetan basket weaving forum. Of course basket weavers will want to analyze how an infinite weave of strings can't be compared to an unwoven infinite string.