### Re: The seven step-Mathematical preliminaries 2

Marty, On 07 Jun 2009, at 02:03, Brent Meeker wrote: m.a. wrote: *Okay, so is it true to say that things written in EXTENSION are never in formula style but are translated into formulas when we put them into INTENSION form? You can see that my difficulty with math arises from an

### Re: The seven step-Mathematical preliminaries 2

: Re: The seven step-Mathematical preliminaries 2 m.a. wrote: *Okay, so is it true to say that things written in EXTENSION are never in formula style but are translated into formulas when we put them into INTENSION form? You can see that my difficulty with math arises from an inability

### Re: The seven step-Mathematical preliminaries 2

Bruno, Yes, this seems very clear and will be helpful to refer back to if necessary. m.a. - Original Message - From: Bruno Marchal marc...@ulb.ac.be To: everything-list@googlegroups.com Sent: Sunday, June 07, 2009 4:33 AM Subject: Re: The seven step-Mathematical

### Re: The seven step-Mathematical preliminaries 2

: Bruno Marchal To: everything-list@googlegroups.com Sent: Wednesday, June 03, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2 ? ? A = ? ? B = A ? ? = B ? ? = N ? ? = B ? ? = ? ? B

### Re: The seven step-Mathematical preliminaries 2

: The seven step-Mathematical preliminaries 2 ∅ ∪ A = ∅ ∪ B = A ∪ ∅ = B ∪ ∅ = N ∩ ∅ = B ∩ ∅ = ∅ ∩ B = ∅ ∩ ∅ = ∅ ∪ ∅ = http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received

### Re: The seven step-Mathematical preliminaries 2

Marty, Kim, I realize that, now, the message I have just sent does not have the right symbols. Apparently my computer does not understand the Thunderbird! From now on I will use capital words for the mathematical symbols. And I will write mathematical expression in bold. For examples:

### Re: The seven step-Mathematical preliminaries 2

To: everything-list@googlegroups.com Sent: Wednesday, June 03, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2 ∅ ∪ A = ∅ ∪ B = A ∪ ∅ = B ∪ ∅ = N ∩ ∅ = B ∩ ∅ = ∅ ∩ B = ∅ ∩ ∅ = ∅ ∪ ∅ = --- To unsubscribe from this group, send email

### Re: The seven step-Mathematical preliminaries 2

, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2 ∅ ∪ A = ∅ ∪ B = A ∪ ∅ = B ∪ ∅ = N ∩ ∅ = B ∩ ∅ = ∅ ∩ B = ∅ ∩ ∅ = ∅ ∪ ∅ = --- To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit

### RE: The seven step-Mathematical preliminaries 2

If it helps, here's a screenshot of how the symbols are supposed to look: http://img34.imageshack.us/img34/3345/picture2uzk.png From: marc...@ulb.ac.be To: everything-list@googlegroups.com Subject: Re: The seven step-Mathematical preliminaries 2 Date: Sat, 6 Jun 2009 22:36:01 +0200 Marty, Bruno

### Re: The seven step-Mathematical preliminaries 2

Marchal To: everything-list@googlegroups.com Sent: Saturday, June 06, 2009 4:36 PM Subject: Re: The seven step-Mathematical preliminaries 2 We do have problem of symbols, with the mail. I don't see any rectangle in the message below! Take it easy and . We will go very slowly

### Re: The seven step-Mathematical preliminaries 2

To: everything-list@googlegroups.com Sent: Wednesday, June 03, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2 === Intension and extension In the case of finite and little set we have seen that we can define them

### Re: The seven step-Mathematical preliminaries 2

- From: Bruno Marchal To: everything-list@googlegroups.com Sent: Wednesday, June 03, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2 ∅ ∪ A = ∅ ∪ B = A ∪ ∅ = B ∪ ∅ = N ∩ ∅ = B ∩ ∅ = ∅ ∩ B = ∅ ∩ ∅ = ∅ ∪ ∅ = --- To unsubscribe from

### Re: The seven step-Mathematical preliminaries 2

expression just slip out from my mind. smaller than is much better! Thanks for helping, Bruno - Original Message - From: Bruno Marchal To: everything-list@googlegroups.com Sent: Wednesday, June 03, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2

### Re: The seven step-Mathematical preliminaries 2

On this date, you made the following correction: You cannot write D = 4*x ..., But you wrote D= 4*x in the exercise just above it. I don't get the distinction between your use of the equation and mine. - Original Message - From: Bruno Marchal Exercise 2: I will

### Re: The seven step-Mathematical preliminaries 2

m.a. wrote: *Bruno,* * I've encountered some difficulty with the examples below. You say that in extension describes exhaustion or quasi-exhaustion. And you give the example: **B = {3, 6, 9, 12, ... 99}.* * Then you define in intension with exactly the same type

### Re: The seven step-Mathematical preliminaries 2

Bruno, When I tried to copy the symbols from the URL cited below, I found that my email server was not able to reproproduce the intersection or the union symbol. See below: From: Bruno Marchal To: everything-list@googlegroups.com ∅ ∪ A = I see two

### Re: The seven step-Mathematical preliminaries 2

Okay, so is it true to say that things written in EXTENSION are never in formula style but are translated into formulas when we put them into INTENSION form? You can see that my difficulty with math arises from an inability to master even the simplest definitions.marty a. -

### Re: The seven step-Mathematical preliminaries 2

m.a. wrote: *Okay, so is it true to say that things written in EXTENSION are never in formula style but are translated into formulas when we put them into INTENSION form? You can see that my difficulty with math arises from an inability to master even the simplest definitions.

### Re: The seven step-Mathematical preliminaries 2

Hi Marty, On 05 Jun 2009, at 00:30, m.a. wrote: Bruno, I don't have dyslexia Good news. but my keyboard doesn't contain either the UNION symbol or the INTERSECTION symbol Nor do mine! (unless I want to go into an INSERT pull down menu every time I use those

### Re: The seven step-Mathematical preliminaries 2

10:03 AM Subject: Re: The seven step-Mathematical preliminaries 2 Hi Marty, On 05 Jun 2009, at 00:30, m.a. wrote: Bruno, I don't have dyslexia Good news. but my keyboard doesn't contain either the UNION symbol or the INTERSECTION symbol

### Re: The seven step-Mathematical preliminaries 2

On Thu Jun 4 1:15 , Bruno Marchal sent: Very good answer, Kim,  Just a few comments. and then the sequel. Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,   3, ...}? No idea what square-root(2) means. When I said I was innumerate I wasn't kidding! I could of

### Re: The seven step-Mathematical preliminaries 2

Hi Marty, On 04 Jun 2009, at 01:11, m.a. wrote: Bruno, I stopped half-way through because I'm not at all sure of my answers and would like to have them confirmed or corrected, if necessary, rather than go on giving wrong answers. marty a. No problem. Exercise 1: Could

### Re: The seven step-Mathematical preliminaries 2

On Thu, Jun 4, 2009 at 7:28 AM, kimjo...@ozemail.com.au kimjo...@ozemail.com.au wrote: On Thu Jun  4  1:15 , Bruno Marchal  sent: Very good answer, Kim, Just a few comments. and then the sequel. Exercice 4: does the real number square-root(2) belongs to {0, 1, 2, 3, ...}? No idea what

### Re: The seven step-Mathematical preliminaries 2

Hi Kim, On 04 Jun 2009, at 14:28, kimjo...@ozemail.com.au wrote: OK - I find this quite mind-blowing; probably because I now understand it for the first time in my life. So how did it get this rather ridiculous name of square root? What's it called in French? Racine carrée.

### Re: The seven step-Mathematical preliminaries 2

adjusted to my math disabilities and won't take offence at all. Thanks, marty a. - Original Message - From: Bruno Marchal To: everything-list@googlegroups.com Sent: Thursday, June 04, 2009 12:04 PM Subject: Re: The seven step-Mathematical preliminaries 2 Hi Marty

### Re: The seven step-Mathematical preliminaries 2

Very good answer, Kim, Just a few comments. and then the sequel. Exercice 4: does the real number square-root(2) belongs to {0, 1, 2, 3, ...}? No idea what square-root(2) means. When I said I was innumerate I wasn't kidding! I could of course look it up or ask my mathematics teacher

### Re: The seven step-Mathematical preliminaries 2

@googlegroups.com Sent: Wednesday, June 03, 2009 1:15 PM Subject: Re: The seven step-Mathematical preliminaries 2 === Intension and extension Before defining intersection, union and the notion of subset, I would like to come back on the ways we can define some