Teacher: Other comments about the conjecture?
So right now we saw that so far it looks like we might be able to use different odd numbers.
Did anybody come up with an example that didn't work, for example?
Did anyone find an odd number plus an odd number that didn't equal an even number?
Jeannie, you found one?
Jeannie: Me and Sheena were working together, but we didn't find one that didn't work.
We were trying to prove that Betsy's conjecture- that you can't prove that Betsy's conjecture always works.
Teacher: Go on, Jeannie. Say more about why you think that.
Jeannie: Because there's- like numbers go on and on forever and that means odd numbers and even numbers
go on forever, and so you couldn't prove that all of them worked.
Teacher: What are people's reactions to what Jeannie and Sheena thought?
They said they didn't find one that didn't work,
but they don't think we can prove it always works because numbers go on forever and ever.
Ofala?
Ofala: I think it can always- Teacher: Talk that way.
Ofala: I think it can always work because I tried almost...
Ofala: Eighteen of them, and I also tried a Sean number, so I think... I think it can always work.
Teacher: Mei?
Mei: I think it could always work because with those conjectures
we haven't even tried them with all the numbers that there is,
so why do you say those work? Well, we haven't even tried all those numbers that there ever could be.
Teacher: So, are you agreeing with Jeannie or not?
Mei: I disagree.
Teacher: But I don't understand. You're saying we haven't tried all the numbers, that's what she's...
Mei: Like she's saying that we can't make sure it's working because there's many, many like-
Numbers goes on forever.
Teacher: Yeah.
Mei: Yeah, but we haven't tried- We haven't- She said that it's not always true.
Then why do you say that it's- that those conjectures is not always true?
Teacher: Oh, you're talking about these?
Mei: Uh-huh. But why don't you say that those are true because we haven't tried every number that there was.
So you can't really say that those are true if you're saying that you want to try every number there ever was.
Teacher: Jeannie?
Jeannie: I never said that they were true all the time...
Mei: Then why do- then why didn't you disagree when like Lucy and everybody agreed with those conjectures?
Jeannie: Because I wasn't thinking about it.
Sheena: She just thought about it. That's why we were trying to think about it today to see if it always works.
Teacher: What do other people think about what Jeannie's saying?
Do you think we can't prove that it's always true, or do you think that we can prove that it's always true?