/sci/ - Science & Math

[Anonymous No.9629848]

Why is the first figure (left) not a function? By definition?

[Anonymous No.9629854]

>By definition?
Yes.

[Anonymous No.9629860]

1 input can't have 2 outputs

[math]
\sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right |
[/math]

[Anonymous No.9629870]

Functions aren't allowed to fan out, only fan in

[Anonymous No.9629886]

Think about it

Its the only thing that separates a relation from a function

3 <4 yes but also 3<5, 3 <6.....

But if f: R -> R (maps real numbers to real numbers)
And f (x)=x^2

This is a function. Every x not only has an output but at most one output .
No arrows "fan out" from the input and all inputs have an arrow

This is also an injective function (one-to-one). I'll let you figure out why. You should also check if it is surjective (onto) or not.

[Anonymous No.9629910]

>>9629886
>This is also an injective function (one-to-one)
f(-2)=f(2)=4

[Anonymous No.9630155]

>>9629848
Functions need to be continuous

[Anonymous No.9630638]

>>9630155
No, they don't, are you actually retarded?

[Anonymous No.9630685]

There are no functions that can output different results with the same input

[Anonymous No.9630707]

>>9630155
Holy kek. Being this stupid.

[Anonymous No.9630714]

>>9630638
>>9630707
Continuous means that given the same input they need a different output

[Anonymous No.9630716]

>>9630685
How about a square root making a positive and negative number?

[Anonymous No.9630719]

>>9630714
Is English your native language? Serious question, because I don't understand what you're saying.

[Anonymous No.9630721]

>>9630716
That's not what happens. Given an equation sqrt(x) == a, x can be +a or -a. However, sqrt(x) will then always be +a, never -a.

[Anonymous No.9630722]

>>9629848
functions take one input and produces 1 output

>>9630714
That's not what continuity means in mathematics

literally google it

[Anonymous No.9630728]

>>9630716
Nope

sqrt(a^2) = |a| = a

For example

sqrt(+3^2) = |+3| = 3
sqrt(-3^2) = |-3| = 3
Different input, same output

[Anonymous No.9630741]

>>9630728
>sqrt(a^2) = |a|
Since when?

[Anonymous No.9630743]

>>9630741
Since the definition of square root

[Anonymous No.9630753]

>>9630743
The inverse of a square root is not necessarily a positive number unless it's the square root of a real number.

[Anonymous No.9630755]

How about lambert W having 2 or even 3 outputs for a significantly low input?

[Anonymous No.9630775]

>>9630714
Imagine being this retarded

[Anonymous No.9630782]

>>9630716
Square roots defined over complex numbers are not functions you absolute mongoloid

[Anonymous No.9631425]

>>9630155
You must be at least 18 to post on 4chan.

[Anonymous No.9632377]

>>9630155
Fuck off Brouwer.

[Anonymous No.9632416]

>>9630716
>>9629860