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Topic: Is (t^2-9)/(t-3) defined at t=3?
Replies: 166   Last Post: Oct 30, 2013 9:41 AM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Oct 10, 2013 3:57 PM
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On 10/10/2013 2:24 PM, Arturo Magidin wrote:
> On Wednesday, October 9, 2013 4:51:11 PM UTC-5, fom wrote:
>> On 10/9/2013 12:29 AM, Arturo Magidin wrote:
>>

>>>
>>
>>> Which just accomplishes the student lying to him or herself with the complicity of the professor who tells him its doable.
>>
>>>
>>
>>> Look: I don't object not telling a beginning student the whole truth; I **do** object telling him lies.
>>
>>>
>>
>>>
>>
>>
>>
>> Curious statement.
>>
>>
>>
>> Let me ask you about an actual situation.
>>
>>
>>
>> In the logic text I used as an undergraduate the notion of
>>
>> model had been introduced with respect to a "sentence" from
>>
>> a formal language.
>>
>>
>>
>> In Chang and Keisler, models apply to languages as a whole, and,
>>
>> a language is a list of uninterpreted parameters as in universal
>>
>> algebra.
>>
>>
>>
>> To be more clear concerning the first text, a "structure" is
>>
>> a "model" of a sentence if the sentence is "true with respect
>>
>> to a translation under the structure"
>>
>>
>>
>> Note that this is different from "true in a model" in the
>>
>> sense of Chang and Keisler.
>>
>>
>>
>> That is, a sentence may be true in a structure or
>>
>> a structure may be a model of a sentence.
>>
>>
>>
>> In my naivete, the latter suggests that an admissibility
>>
>> criterion applied to structures could influence something
>>
>> like the status of an independent statement. When one
>>
>> speaks of a model for a language, that notion does not
>>
>> suggest itself.
>>
>>
>>
>> Does this distinction appear legitimate to you?

>
> I'm afraid I do not know enough about the topic to offer an informed opinion, and I confess I don't feel like trying to think through what you are describing at length right now.
>
>

>> If so, has the student been told a lie?
>
> From what you say, what you found *suggested* something to you that is inaccurate, but it did not actually make a false claim; the suggestion arose from your interpretation of what you were given, rather than being something you were explicitly told. If this is the case, then I would not interpret it as a lie.
>


Thank you.

It is an extremely subtle point. Even with respect to
presentation, it could be attributed to a difference of opinion.

But, as with the discussion motivating your remark, it occurred
in an introductory text.




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9/28/13
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Hetware
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10/13/13
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fom
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fom
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9/29/13
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10/16/13
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