Question

Prove If x>y and y>z then x>z

Answer 1

prove transativity..

Answer 2

x > y
y> z

you can substitute y > z into y

=> x > z

Answer 3

not sure if that is a proof...but looks good:)

Answer 4

you can also do this...

rewrite x > y as y < x

y < x
y > z

multiply -1 to first equation

-y > -x
y > z

add the two equations

0 > -x + z

add x to both sides

x > z

Answer 5

does that make sense?

Answer 6

x > y and y > z

by transitive property of inequality

x > z

Answer 7

thanks @lgbasallote! it does

Answer 8

hehe @ganeshie8 I think you defined something with its own deffinition

Answer 9

as in u of o ducks? @iheartducks ?

Answer 10

hit enter @ParthKohli I want to see what you are saying:)

Answer 11

If \(x >y\), then \(x - n_1 = y\).
If \(y>z\), then \(z +n_2 = y\).
Note that \(n_1\) and \(n_2\) are POSITIVE.
Substituting,\[x - n_1 > z + n_2\]Add n1 to both.\[x > z + n_2 + n_1\]Since \(x\) is greater than the sum of \(z\) and two positive numbers, we already know that \(x>z\).

Answer 12

Think about it. If a number is greater than another number + positive number 1 + positive number 2, then the number is greater than the other number ALWAYS.

Answer 13

yeah its easy to see its true, but proofs of easy things are not easy:)

prove 1+1 = 2

Answer 14

I'd like some examples with that:\[\large\underbrace{6}_x>\underbrace{2}_z + \underbrace1_{n_1} + \underbrace2_{n_2}\]\[\implies \underbrace6_x > \underbrace2_z\]

Answer 15

I KNOW its true, i just have difficulty proving it. I can't exactly just plug in numbers. I have to assume my students dont understand anything AT ALL. Thanks for having my back @zzr0ck3r. But @ParthKohli your response helped a lot too. Thanks everyone!

Answer 16

It's a work of intuition. If either of \(n_1\) or \(n_2\) were negative, then the proof would not have been valid.

Answer 17

@iheartducks Remember, you can't just "assume" things in proofs ;)

Answer 18

depends on the proof actually, we assume things in most proofs. you assumed something on the last line.

Answer 19

Where exactly?

Answer 20

indeed. proofs tends to be assumptions at times

Answer 21

It's more like a postulate, actually.
If a number \(x\) is greater than \(y\), then \(x = y + \text{some positive number}\)

Answer 22

u of o ducks? lol nah i just like the animal.

Answer 23

completely like \[y\propto x \implies y = kx \]

Answer 24

whats that :/

Answer 25

is it that proportional thingy?

Answer 26

Yes, it is.

Answer 27

:)

Answer 28

yes but transitivity is a prostulate of which you just proved

Answer 29

order axioms

Answer 30

Yes, and that is done through even more simple axioms.

Answer 31

but they all can be proved...

Answer 32

the proof for 1+1 = 2 is 380ish pages

Answer 33

The ugliest proof is for Fermat's Last Theorem.

Answer 34

ha, yeah and it is really more about proving something else..its about proving that japanese dude that killed himself work