Search found 268 matches

by Averroes
Sat Aug 26, 2017 8:12 am
Forum: Aesthetics
Topic: Great Works of Art
Replies: 83
Views: 11354

Re: Great Works of Art

This is an interesting and informative thread, and I express my appreciation for the idea to the author of this thread. Some interesting Picassoes were presented. Pablo Picasso once said: "If I had known there was such a thing as Islamic Calligraphy, I would never have started to paint. I have striv...
by Averroes
Wed Aug 23, 2017 7:51 am
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 1552

Re: need clearer explanation of mathematical induction.

thank you so much for your willingness to help In my way of life and frame of mind, the more I share what I have been given and the more I help others in doing beneficial things, the more I am helped and the more good things I get. So, it is a win-win situation for both of us! Case 1: P has the for...
by Averroes
Tue Aug 22, 2017 5:43 am
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 1552

Re: need clearer explanation of mathematical induction.

ProfAlexHartdegen

If you are still having trouble with this, you can ask more questions. If that be the case, tell me where you are stuck.
by Averroes
Sun Aug 20, 2017 6:45 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 1552

Re: need clearer explanation of mathematical induction.

so in mathematics and mathematical induction: are you hypothesizing a general principle and trying to prove as many cases as possible are applicable? Concerning mathematical induction, in my understanding, what can appropriately be said to be a general principle is the inductive step, and the latte...
by Averroes
Sat Aug 19, 2017 5:58 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 1552

Re: need clearer explanation of mathematical induction.

They talk about proving the basis clause of the first premise then use the second premise as the inductive step which you need to prove is true I'm not clear - is the inductive hypothesis the first premise? - the basis clause? They say it's the antecedent of the inductive step. If you consider the ...
by Averroes
Sun Aug 13, 2017 12:01 pm
Forum: Logic and Philosophy of Mathematics
Topic: help understanding Negation Introduction
Replies: 17
Views: 2572

Re: help understanding Negation Introduction

I can't understand the use of each individual rule. I mean I know you could apply that rule but I don't see why you use the rule. The 'plan' or the 'forest from the trees' if you will. In the example you provided, it was required to prove (U & M) ⊃ S, M & ~S ⊢ ~U The letters are complete sentences ...
by Averroes
Sun Aug 13, 2017 11:29 am
Forum: Logic and Philosophy of Mathematics
Topic: help understanding Negation Introduction
Replies: 17
Views: 2572

Re: help understanding Negation Introduction

Sorry for the crude representation but as you know the forum isn't conducive to writing symbolic logic. The subderivation is offset a bit to clarify what it is: As has already been explained one can use the code tags of the post editor to include white spaces and format the proof accordingly. It de...
by Averroes
Tue Aug 08, 2017 8:27 am
Forum: Logic and Philosophy of Mathematics
Topic: need help understanding truth functional entailment
Replies: 2
Views: 788

Re: need help understanding truth functional entailment

Can someone help me to understand and clarify this? I do not know but I can try share some thoughts with you. It states: A set Γ of sentences of symbolic logic truth functionally entails a sentence P if and only if there is no truth value assignment on which every member of Γ is true and P is false...
by Averroes
Thu Jul 27, 2017 4:45 pm
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2340

Re: How to construct a formal proof?

Yes, the one snafu was a typo. But I tried to do it without DeMorgan's. I thought that (C & D) and (notC & notD) produced the contradiction for my RAA. For (C & D) reduces to C by separation and then (notC & not D) reduces to notC. So C & notC is the contradiction (the same with D and not D). Why i...
by Averroes
Sun Jul 23, 2017 10:36 pm
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2340

Re: How to construct a formal proof?

WHY make an assumption in the first place? Why not? Why not just look at what IS, already an actual fact? And what would that be? 'The sky is blue on a sunny day', expresses a fact in the English language. In formal logic, there is no such fact. In the problem in the OP, what would you consider as ...
by Averroes
Sun Jul 23, 2017 10:14 pm
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2340

Re: How to construct a formal proof?

It depends on what your professor is requiring of you. Do you have axioms and rules of inference or are less formal proofs allowed? If you are working with only modus ponens (including conditional proof): Assume A (whatever follows from assuming A will create a conditional, If A then....) Assuming ...
by Averroes
Sat Jul 22, 2017 7:43 am
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2340

Re: How to construct a formal proof?

I am a “bit” late on this, but some people say, better late than never! If one can find some wisdom in that saying then here goes. One thing to bear in mind in any logical and/or mathematical proofs, is that the first strategy to attempt to prove anything is the reductio ad absurdum. As the mathemat...
by Averroes
Thu Jul 20, 2017 9:35 pm
Forum: Logic and Philosophy of Mathematics
Topic: Patterns upon patterns
Replies: 29
Views: 3087

Re: Patterns upon patterns

I do. In fact that pattern is one of the famous series in math. But before you can see it, factor out the 8. So now we have: 8•1 = 8 8•3 = 24 8•6 = 48 8•10 = 80... Do you recognize the series 1, 3, 6, 10...? This is the famous triangular series and the process I used which led to those numbers I ca...