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/sci/ - Science & Math

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9985608 No.9985608 [Reply] [Original]

Hey /sci/, I'm a new mathematics college student, can you explain why and how the order of logical quantifiers changes the meaning of a proposition?

I mean, if there's a proposition with multiple quantifiers (with 3 or more preferably), how should I read it so that I understand the correct meaning of it?

Pic unrelated.

>> No.9985630

>>9985608
Put a bar over the 0 of 20 to make it 2 followed by infinitely many 0s i.e. [math]\lim_{n\;\to\;\infty} 2\,\times\,10^n \;=\; \infty[/math].

>Forall x, there exists y such that x = y
>There exists y such that for all x, x = y

>> No.9985668

>>9985608
Try the definition of continuity vs uniform continuity:

For all x for all epsilon > 0 there exists delta > 0 s.t. for all y (d(x, y) < delta implies d(f(x),f(y)) < epsilon)

is weaker than

For all epsilon > 0 there exists delta > 0 s.t. for all x for all y (d(x, y) < delta implies d(f(x), f(y)) < epsilon)

The first states that delta can depend on epsilon and x, and only needs to hold for y close to that specific x. The second states that delta can only depend on epsilon, and needs to hold for ANY x and y which are close to one another.

In general, you can usually interpret different orders of quantifiers by how they affect which bound variables are dependent on which.

>> No.9986180
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9986180

>> No.9986182

>>9986180
fucking KEK

>> No.9986184

>>9986180
Based and 2Dpilled

>> No.9986186

>>9985608
For any integer x, there exists an integer y such that y > x. For example, take y = x + 1.

However, it is *not* true that there exists an integer y such that, for any integer x, y > x. A trivial reason is that y cannot be greater than itself.

>> No.9986192

>>9986180
winrar

>> No.9986204

To generalize, just convert the proposition with the quantifiers into a basic english sentence- do it with different orders of the same quantifiers and you'll gain better understanding. You read it based on highest priority and order with respect to the brackets

>> No.9986211
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9986211

>>9985608
I can do it with one.

>>9986180
kek

>> No.9986246

>>9986211
Color the 3 boxes from the "tip" of the 2 downwards so you get a retarded 9 and you have a correct coloring with 4

>> No.9986594
File: 60 KB, 576x507, 1534899053388.png [View same] [iqdb] [saucenao] [google]
9986594

>>9986180

>> No.9986598

>>9986180
/thread

>> No.9986603

>>9986180
Fuck, is this the correct answer? lol

>> No.9986604

>>9986180
the first time i figured this out i fucking flipped my shit

>> No.9986630
File: 974 KB, 2000x2000, 1535839754754.jpg [View same] [iqdb] [saucenao] [google]
9986630

>>9986180
>baiting the pseudo mathematicians feels so good

>> No.9986651

>>9986603
>>9986598
>>9986594
>>9986211
>>9986192
>>9986184
>>9986182
newfags leave

>> No.9986713

>>9986180
>a meme exposing this many newb tards in one thread
reddit has finally saturated and reached peak stupidity thus offloaded its "talent" to /pol which subsequently also reached peak stupidity and offloaded its "talent" to /sci

Circle of life. Where's next?

>> No.9986721

>>9986211
noice tho

>> No.9986728

>>9986651
>>9986713
>nooo I saw this joke 7 years ago so you can't laugh at it newfag!

>> No.9986738

>>9986713
>/sci
>/pol
And then you have the audacity to call someone new and Reddit.

>> No.9986739

>>9985608
80>30

>> No.9987109

>>9986180
This is still wrong though.

>> No.9987441

>>9986713
This is a Japanese website you fucking retard.

>> No.9987609

>>9987441
>Registrant City:Drums
>Registrant State/Province:PA
>Registrant Country:US
>Admin City:Drums
>Admin State/Province:PA
>Admin Postal Code:18222
>Admin Country:US
???

>> No.9987622

>>9987441
How new?

>> No.9987640

>>9987441
You are so dumb. His point is that it's an old meme and all the newfags seeing it for the first time. And it's not a japanese website, it's a western anime website

>> No.9987657

>>9987640
>it's a western anime website
It's a western multi-topical website.

>> No.9987673

>>9986739

this

>> No.9987677

>>9987657
My little pony websites are multi-topical, but that doesn't mean they're not my little pony websites

>> No.9987680
File: 478 KB, 1126x1746, quantifiers.jpg [View same] [iqdb] [saucenao] [google]
9987680

>> No.9987685

>>9987677
But on MLP websites, it's written on the front page that it's an MLP website.

>> No.9987957
File: 267 KB, 530x549, CutPaste_2018-09-08_21-13-26-330.png [View same] [iqdb] [saucenao] [google]
9987957

OP here, thanks for your replies.

>> No.9987968

>>9987957
Good thread OP

>> No.9988051

>>9986180
and here I was thinking you had to make the 2 an 8

>> No.9988057

>>9987680
this is actually really helpful

>> No.9988358

>>9985608
20 > 3.0

one dot

>> No.9988509

>>9986180
Genius.

>> No.9988528

>>9985608
30 becomes 3.0 by filling in one box.
I win, where's my prize

>> No.9988530

>>9988528
It says to fill 4 boxes, not 1

>> No.9988735

>>9988530
not my problem the 3 other boxes were already filled in

>> No.9989017
File: 387 KB, 800x800, 63219819_p0.jpg [View same] [iqdb] [saucenao] [google]
9989017

>>9987109
You're the one who's wrong here. That anon speaks the truth.

>> No.9989039

>>9986180
I'm impressed.