Okay

so last time we started looking at math talk for statements after having talked about

math talk for objects.

Are there any questions?

Yes.

It is allowed to go back

yes.

I've heard about that from a quiz that may be something that may be a regression.

I'm not sure

I think as far as I understand

whatever you did is safe with the system

so you're not losing the old answers.

But it basically cleans the slate.

Whether that's the ideal thing to do, I don't know.

It obviously seems to be surprising.

So yes.

And also one more thing about last week's quiz, there was one question that needs to

be re-corrected.

Everybody got that wrong.

Actually I got that wrong, therefore you didn't get the credit you deserve.

I haven't been able to do that yet

but we will.

Okay.

So we're still looking at mathematical language.

We basically have three levels at which we can look at mathematical language.

The level of objects

things like three or five or the structure of groups or all of

those kind of things.

Then the level of statements

the objects are things that are just things that are around

in math.

These are things that are true or false, and we're talking about those.

And here we basically have the axioms of natural numbers

the piano axioms.

Those are true by definition

because we say so.

Those axioms are one of these kind of multiple forms in which statements can exist.

And we've kind of looked at these funny symbols that are just abbreviations for certain things.

Inverted A is A for all.

And it binds, as we've seen, the X.

And ranges over a whole range of things

possibly.

And in this case

the N is the bound variable

the ranges over the unary natural numbers.

Right?

We're not giving element N1 the variable ranges over the whole universe

everything.

At the object side

we have variables.