Checking your reasoning

Let's state the obvious. First, we `assume x < 0`. Then we can surely conclude (drum roll) that `x < 0`!

Passing your first quiz

The document above contains two meaningful mathematical expressions. You know that they are meaningful (not just expository) because of the blue borders. But Lurch has not yet given any indication of whether the (very simple!) reasoning in the above document is correct. Let's make that happen.

Exercise: Ask for a grade

  1. In the document shown above, click the Document menu and choose "Check my reasoning."
  2. You should find that the second meaningful mathematics gets a green check mark from Lurch, your virtual grader.
  3. Hover your mouse pointer over that green check mark. You should see Lurch give you some small positive feedback ("Good work!").

Throwing the game

Let's make a mistake to be sure that Lurch isn't practicing grade inflation. If we do something mathematically invalid, it ought to make an error.

Exercise: Oops

  1. In the same document you see above, click the second expression to edit it.
  2. Change its meaning from \(x<0\) to \(y<0\) and click OK.
  3. Note that all feedback has disappeared from your document. When you make an edit, Lurch is aware that its previous feedback may no longer apply, and it erases it.
  4. Ask Lurch to check your reasoning again, and then use your mouse to hover over the feedback icon for more information.

You'll notice that Lurch doesn't tell you that you're wrong. This is appropriate because Lurch doesn't want to jump to conclusions. After all, maybe \(y<0\) and maybe it isn't--we haven't specified! So Lurch just lets you know that you haven't provided any evidence to support this conclusion. Whether it's true or false is another matter--Lurch is just reading the evidence you've provided (or failed to provide).

Questions?

This exercise may have raised many questions in your mind, such as how the first expression counts as an assumption, why it didn't get any feedback attached to it, and what are the limits of Lurch's mathematical knowledge. We will cover all of those things in this tutorial, one at a time.

Let's start with learning about assumptions.