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/sci/ - Science & Math

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7510562 No.7510562 [Reply] [Original]

I know homework is looked down upon here at /sci/, but I wanted confirmation on this quick and dirty proof.

I need to prove "if x < y + ε for all ε > 0, then x ≤ y".

Here are my steps, please tell me if this makes sense and is mathematically sound:

1) Assume for contradiction that x < y + ε for all ε > 0 and x > y.

2) Let ε = x - y; We know x - y > 0 because of our assumption.

3) x < y + ε

4) x < y + (x - y)

5) x < x + 0

6) x < x, which is not possible;

Thus a contradiction has been reached and the statement "if x < y + ε for all ε > 0, then x ≤ y" must be true. QED.

>> No.7510565

>>7510562
it's fine anon

>> No.7510584

>>7510562
It's perfect.

>> No.7510585

>>7510565
>>7510584
Thanks anons. I'm terrible at this stuff and Real Analysis has been blowing my mind this first week of class.

>> No.7510588

nice babby analysis OP

now gtfo of there and do some elegant algebra for your mind is polluted with the analytical satan

>> No.7510592
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7510592

>>7510588

>> No.7510614

In your proof, the premise 2) is based on is contradicted by 1). Your proof is invalid.

Instead, go 0 > y - x and make that a compound inequality with ε > 0 > y - x. Therefor ε > y - x, and it should be pretty easy to reach a contradiction from there.

If you don't understand why your proof is invalid, just do it my way anyways, since you can definitely see why my way works as well.

>> No.7510616

>>7510585
I start this shit Thursday. So excited Anon. Seeing that it has been blowing your mind, I'm even more excited now.

>> No.7510619

>>7510614
he's just reusing the symbol epsilon

>> No.7510628

>>7510619
This, OP is fine.

>> No.7510629

>>7510619
OP's proof only proves it for the case when ε = x - y. For ε = x - y + 1, 6) is true.

>> No.7510632

Why would anyone need to prove this? This is why I dropped out. Fucking bureaucracy

>> No.7510633

>>7510629
The case is for ALL epsilon, so he only has to show that one particular epsilon would give a contradiction

>> No.7510641
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7510641

>>7510629

>> No.7510642

>>7510562
Doesn't having to "prove" this imply you don't understand it? I mean, what the fuck, this is worse than edgelords

>> No.7510655
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7510655

>>7510642
>what is math

>> No.7510670
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7510670

>>7510655
This is not math, I am sorry.
It just implies you don't understand basic arithmetic/logic, this is just some monkey dance for a degree

>> No.7510676
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7510676

>>7510670

>> No.7510695

>>7510642

>Cant tell if arrogant Logician or pleb

>Cant tell which is worse

>We know you dont have friends anyway

>> No.7510697

>>7510633

Oh. Lol, I see it now. OP's proof is legit. Thanks for explaining.

>> No.7510702

>>7510585
>real analysis
i thought this was beginner logic/discrete math class

>> No.7510731

>>7510702
it's the first few weeks mate, they're probably going over basics

>> No.7510753
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7510753

>>7510562
>contradiction
Fucking mindless ape...

If you already realised ε = x - y
Just say ε = x - y
x < y + ε for all ε > 0, then x ≤ y + x - y
x ≤ x

If you really want to prove it: Where is the ε = x - y coming from? x - y > 0? Well, if "if x < y + ε for all ε > 0, then x ≤ y" is not clear, then "x - y > 0 therefore ε = x - y" is not understood either. Fucking ape.

>> No.7510756
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7510756

>>7510753
this might be the most mind-numbingly stupid thing I've ever read.

>> No.7510758
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7510758

not OP .. but homework thread.. decided to self study physics and i dont get pic related. Where does 1.6 come from? Can anyone help me out?

>> No.7510776

>>7510758
The handle goes around 1260 inches to lift 1 inch. 2000 pounds / 1260 = 1.5873 = 1.6 lb

You are fucking stupid and HW could yield you a ban.

>> No.7510790

>>7510753
This is right. I am out of here, /sci/ is fucking shit.

>> No.7510792
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7510792

>>7510790
what?