/sci/ - Science & Math

What's your favorite argument in a proof?

Mine is Cantor's diagonal argument. It is simple, and makes you shit a brick when you see how versatile and powerful it is.

>>8333166
>Descartes, Spinoza, Leibniz
>Renaissance

>>5414622
>implying that this won't make him a social shut-in

>ebin served

gebnius op 10/10 nobell peace price

>>5221202
>implying people care who you really are
I'm sure they just want to know that someone here has actually patented something and isn't a highschool pleeb.

>>5204138
>implying that molecules are not colliding if you can't see them

>hey sci, can you tell me whether this proof is right or wrong?
<div class="math">\lim_{x\to a}x^4=a^4</div>
<div class="math">0<|x-a|<\delta \Rightarrow |x^4-a^4|<\epsilon</div>
factorising the epsilon part gives us
<div class="math">|x-a||x+a||x^2+a^2|<\epsilon</div>
NOw if we set delta<1, then
<div class="math">|x^4-a^4|<\delta|x+a||x^2+a^2|</div>
since a-1<x<1+a,adding a gives us <span class="math"> 2a-1<x+a<1+2a [/spoiler]
and for the <span class="math">x^2+a^2[/spoiler] term, we can just square and add <span class="math"> a^2 [/spoiler] to both sides.
Therefore, the final inequlaity is
<div class="math">|x^4-a^4|<\delta|2a+1||(a+1)^2+a^2|</div>
which simplifies into
<div class="math">=\delta(4a^3 +2a^2-1)</div>
If we set this equal to epsilon, we get
<div class="math">\frac{\epsilon}{(4a^3 +2a^2-1)}=\delta</div>

>am I wrong anywhere?

Sup sci, i need help with this question.
Let <span class="math"> [x] [/spoiler] denote the largest integer <span class="math"> \le x [/spoiler]. Thus, if <span class="math"> n \le < n+1 [/spoiler], then <span class="math"> [x]=n [/spoiler]. What will the graph of the function <span class="math">f(x)=x-[x]-\frac{1}{2} [/spoiler] look like?