#bijective

[arcsin27]

if youre bisexual youre also insexual and sursexual

[lesbianslovebts]

My therapist asked me to explain what my autistic brain does when studying languages, and I answered, "Math." She didn't quite get it, but it really is math! When I see the same sentence in different languages, it's like solving an algebraic equation. And I love how translation can be surjective, injective, or bijective! Korean and Japanese are as close to a grammatical isomorphism as you can get, in my opinion.

나는 친구하고 같이 공원에 점심을 먹으러 갔었어요.

私は友達と一緒に公園に昼ごはんを食べに行きました。

As opposed to English:

I went to the park with my friend to eat lunch.

[isomorphismes]

the pigeonhole principle, as applied to the enter() and data() verbs of d3.js

by Sebastian

[sciencesolutions]

[sciencesolutions]

[jarnowouda]

Surjective, injective and bijective

Surjective, injective and bijective

1. Introductie 2. Afbeelden 3. Injectief 4. Surjectief 5. Bijectief

ENGNL

Coming soon-ish… If that isn’t soon enough, just leave a comment below! 😉 Share on pinterest Share on facebook Share on twitter Share on linkedin Share on tumblr 1. Introductie

Een functie kan injectief, surjectief en bijectief zijn. In deze post behandelen we wat deze begrippen betekenen en onderscheiden we…

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[fardell24b]

Math 101 Lecture 13 revision

Math 101 – Lecture 13 revision

Surjective if for every b € Range of there is at least one a a motif at f(a) = b

Injective if for every b there is at most one a at f(a) = b

              If injective and surjective then f is bijective

e.g. (1) f |R -|R

              f(x) = x

http://u.cubeupload.com/Brenorenz/surjectiveinjective1.png

 Bijective

 (2) f: |R -> {0, 1)

 f(x) =      {o, x irrational

              {I, x rational

Not injective

Is surjective

(3)

 http://u.cubeupload.com/Brenorenz/surjectiveinjective2.png

 f: |N à |R

f(x) = x2 – 1

 not surjective

is injective

 -//-

 Limits

Notions f(x) approaches some value  /_ as x approaches some value c € Domain f

              Indicate by f(x) à L as x à c

 Or          lim f(x) = L

              X ->

              The closer I get to x = L the closer x gets to L

 Approximation

              Given a degree of approximation |f(x) – L ) < 0.01

                             Can you find the x that gives this approximation?

                             eg f(x) = x2 à 1 as x à 1

                             Given the approximation |x2 - 1| < 0.01

                             Can we find the possible x’s?

                             Solution |x2 - 1| < 0.01

                             Means -0.01 < x2 – 1 < 0.01

                             Ie 0.99 < x2 < 1.01

                                            ∴ √0.99 < x < √1.01

                                            ∴ |x2 - 1| < 0.01 whenever √0.99 < |x| < √1.01

 Formal Definition of a Limit

We say f(x) à L as x à c or

Lim

xà c

  If given any ℇ > 0 there is a δ > 0 such that |f(x) = L| < ℇ whenever |x - L| < ℇ

Means given the approximation ℇ : - |f(x) - L| < ℇ

We have to find the δ (depend on          ) to make |f(x) - L| < ℇ whenever |x - c| < δ

eg (a) Prove x2 à 1 as x à 1

 Solution: Let ℇ > 0 be given we must find a δ such that |x2 - 1| < ℇ whenever |x – 1| < δ

We must find the approximate δ

Now |x2 - 1|       = |(x - 1)(x + 1)|

                             = |x - 1||x + 1| < |x + 1|

              Also (x - 1) < δ, - δ < x – 1 < δ

              ie 1 – δ < x < 2 + δ

              ∴ 2 – δ < x + 1 < 2 + δ

              Choose δ < 1, then |x + 1| < 3 and 3 δ

              |x2 – 1| < δ |x + 1| < 3 δ Now choose δ ≤ 1/3 ℇ

                             Then |x2 – 1| ≤ €ℇ whenever |x – 1| < δ < ℇ/3