By Andy Liu

Arithmetical Wonderland is meant as an unorthodox arithmetic textbook for college kids in ordinary schooling, in a contents direction provided through a arithmetic division. The scope is intentionally constrained to hide merely mathematics, even supposing geometric components are brought every time warranted. for instance, what the Euclidean set of rules for locating the best universal divisors of 2 numbers has to do with Euclid is showcased. Many scholars locate arithmetic just a little daunting. it's the authors trust that a lot of that's brought on no longer via the topic itself, yet by way of the language of arithmetic. during this e-book, a lot of the dialogue is in dialogues among Alice, of Wonderland status, and the twins Tweedledum and Tweedledee who hailed from during the taking a look Glass. the men are studying excessive mathematics or user-friendly quantity thought from Alice, and the reader is carried alongside during this educational exploration. therefore many formal proofs are switched over to soothing daily language. however, the e-book has substantial intensity. It examines many arcane corners of the topic, and increases particularly unorthodox questions. for example, Alice tells the twins that six divided by means of 3 is 2 basically due to an implicit assumption that department is meant to be reasonable, while equity doesn't come into addition, subtraction or multiplication. a few subject matters usually now not coated are brought fairly early, similar to the techniques of divisibility and congruence.

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**Extra info for Arithmetical Wonderland**

**Sample text**

There is an extra plum because the last one on the top row will land outside the cake. 4. Determine all possible dimensions of a cake that can be cut completely into the Unicorn’s pieces.

By the Anti-symmetric Property of ≤, we have a = b. This last property is somewhat more involved than the first two. So we will consider it in several stages. 4. If 3 divides 9 and 9 divides 36, prove that 3 divides 36. Solution Since 36 = 3 × 12, 3 divides 36. Note that we do not need the given information at all. This is an unfortunate consequence of using only numbers, as we often end up short-circuiting the situation and failing to provide the intended illustration. 5. If 3 divides 9 and 9 divides a certain positive integer c, prove that 3 divides c.

B) Find the value of x for which f (x) = g(x). 5. Compute ((−3) − (−4)) × (3 + (−8)). 6. Compute (3 − (−7)) × (6 − 3). 7. Compute ((−3) − 6) × ((−3) + (−5)). 8. Compute ((−5) + (−4)) × (7 − (−3)). 9. The sum of two of 1, 2, 4 and 9 minus one of the remaining two numbers is a negative integer. Find the number of possible values of this negative integer. 10. The sum of two of 1, 2, 3 and 5 minus one of the remaining two numbers is a positive integer. Find the number of possible values of this positive integer.

### Arithmetical Wonderland by Andy Liu

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