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Re: MLCS Webinar on April 24: Registration Open
Posted:
Apr 12, 2012 8:31 AM
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But please see http://en.wikipedia.org/wiki/Linear_function
(hope I typed it correctly, if not, it can be googled)
My universe is developmental math, so I need f(x) = ax + b as the definition
of a linear function for my students.
Phil
On 4/12/12 7:01 AM, "Alain Schremmer" <schremmer.alain@gmail.com> wrote:
>
> On Apr 11, 2012, at 10:11 PM, Guy Brandenburg wrote:
>
>> What if some folks don't buy that definition?
>
> Then their students will be confused if and when they get to any kind
> of "linear mathematics", e,g, "linear algebra" and, in fact, already
> when they get to (multivariate) calculus: In f(x_0+h) = f(x_0) +
> f'(x_0) h + [...] , f(x_0) + f'(x_0) h is the affine part (the
> tangent) while f'(x_0) h is the linear part.
>
> See for instance
>
> <http://cfsv.synechism.org/c1/sec15.pdf>,
> <http://mathworld.wolfram.com/AffineFunction.html>,
> <http://www.businessdictionary.com/definition/affine-function.html>.
> <http://economics.about.com/cs/economicsglossary/g/affine.htm>
> <http://www.wolframalpha.com/entities/mathworld/affine_function/j7/hf/yw/
>>
> <http://medialab.di.unipi.it/web/IUM/Waterloo/node37.html>
>
> Regards
> --schremmer
>
>
>> Guy
>>
>> On Apr 11, 2012, at 9:55 PM, Alain Schremmer <schremmer.alain@gmail.com
>>> wrote:
>>
>>> (1) Definition: A function f is linear if and only if
>>>
>>> f( m_1x_1 + m_2x_2) = m_1f(x_1)+m_2f(x_2)
>>>
>>> (The output of a linear combination of inputs is the linear
>>> combination of the outputs. In other words, the diagram commutes,)
>>>
>>> (2) The function x > f(x) = ax+b is NOT linear (It is called
>>> AFFINE)
>>>
>>> (3) The function x > f(x) = ax IS linear
>>>
>>> Regards
>>> --schremmer
>
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