/sci/ - Science & Math

[Anonymous No.5137922]

Would anybody be able to help me convert this statement into lower predicate calculus? I tried /b/, but I got no help there. I'm new at it, and I don't want to get further into the book before I can understand this basic part:

"For every number there is always a greater number"

I've been coming up with ›››(∃x (Px ⊃ Qx)), but something tells me I'm wrong.

Any help? Please?

[kairos !gT31ceG48I No.5137933]

Do you guys use ⊃ to mean less than? Usually that means proper subset, with > meaning less than.

Also note that your sentence says "there is some P(x) that is a subset of Q(x)"

Are you talking about SOME numbers?

[kairos !gT31ceG48I No.5137939]

>>5137933
Or rather, < meaning less than.

[Anonymous No.5137947]

>>5137933

In this case, ⊃ stands as an if...then.

Thanks for catching my existential quantifier, I should replace that with the universal quantifier. Every time I go to revise what I've put down, I get sent into a spiral of confusion.

[Anonymous No.5137972]

>>5137922
I do not know what symbols you are using for your predicate calculus but here is one way of writing your statement:
∀x∃y(x<y)
Once again, I do not know the conventions of your book so I do not know if this is what you are looking for.

[Anonymous No.5137994]

>>5137972

Ah! As soon as I read it, it makes sense.

As long as your use of < stands as an indicator of causality, right? For example, the truth table for ⊃ in propositional calculus (which is still used in predicate calculus) is

a ⊃ b
1 1 1
1 0 0
0 1 1
0 1 0

Are we using the same meaning, but just with different symbols?

Either way, I thank you immensely for your help.

[Anonymous No.5138003]

>>5137922
For all numbers x in Set R, there exists a number y in set R, such that x<y

Now just use quantifiers.

\thread

[Anonymous No.5138005]

>>5137994
>As long as your use of < stands as an indicator of causality, right?

lolwut

His statement reads "For all x, there exists y such that x is less than y." That's all.

[Anonymous No.5138013]

Can't you just, for any number x, there x+1 is a greater number?

[Anonymous No.5138015]

Try reddit's logic subreddit. Gets shit done more often than not, even homework threads

[Anonymous No.5138019]

>>5138005

I know that, but in the predicate calculus I have encountered, there has been no "less than" symbol. So far, everything has been done with the "and", "or", "is equivalent to", "not", and "leads to" signs. These signs are not standardised, and so I was wondering is the "<" was another way of writing "⊃".

I don't mean to argue, as my knowledge is so limited. I appreciate all the help I am getting in this thread.

[Anonymous No.5138023]

>>5138015
Ops, forget that, >>5137972 got it right.

[Anonymous No.5138050]

>>5138019
>I was wondering is the "<" was another way of writing "⊃".

No, not even close.
The problem is that "<" is not defined right off the bat. It actually takes some work to define "<". It also only applies to certain types of sets. I doubt you are capable of defining all that shit, since you didn't even know the difference between "<" and "⊃". Just use >>5137972 and assume the "<" relation is already defined for you.

[Anonymous No.5138058]

<span class="math">
\forall x \in\mathbb{Z} (\exists y \in\mathbb{Z} / x < y )
[/spoiler]
That's how I'd put it, and I study mathematics
(I hope the latex went well, I just learnt how to use it)

[Anonymous No.5138064]

>>5138058
>That's how I'd put it, and I study mathematics
>(I hope the latex went well, I just learnt how to use it)

[Anonymous No.5138066]

>>5138058
And I forgot to say, I said that statement for Z (Integers), but you could say the same about naturals or reals (or any subset of reals that has no maximum).
That's why I like mathematical statements, in english (or spanish or chinese) you can say statements that have two or more interpretations, but mathematical language is a much more specific and correct one.

[kairos !gT31ceG48I No.5138072]

>>5138013
Not an equivalent statement, though similar.

The cat's out of the bag now, but OP your biggest problem seems to be getting used to using multiple variables and qualifiers. Neither one "for all" nor one "for some" would have served you here.

[Anonymous No.5138079]

>>5138064
Second year here, and I'm just learning latex because I'm taking a computer science course.. If I wasn't, I could learn latex in a year. We do real maths before acknowledging computers even exists.

[Anonymous No.5138090]

>>5138013
You would use induction to prove this statement, you would not use induction to write it in the formal language.

[Anonymous No.5138095]

>>5138050

I knew the difference between < and ⊃, but since < isn't actually used in predicate logic ( I can't find a reference to it anywhere), I assumed it may have been an alternate signage.

[Anonymous No.5138105]

>>5138072

Thanks. I really can't understand why that didn't occur to me sooner. I'm a bit intimidated by the step up from the easy nature of propositional calculus into the more involved nature of LPC.

[Anonymous No.5138117]

>>5138105

And by sooner, I meant "at all"