By A. Grothendieck

ISBN-10: 0387056475

ISBN-13: 9780387056470

**Read Online or Download SGA 6: Theorie des reductions et theoreme de Riemann-Roch PDF**

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**Extra info for SGA 6: Theorie des reductions et theoreme de Riemann-Roch**

**Example text**

3) ϩ (ϩ8) ϭ ϩ5 (ϩ2) ϩ (Ϫ4) ϭ ? Pretend both numbers are positive and subtract the smaller number from the larger number. 4Ϫ2ϭ2 Give the answer the sign of the larger number if both numbers were positive. Four is larger than two and it is negative, so the answer is negative. (ϩ2) ϩ (Ϫ4) ϭ Ϫ2 46 algebra_ch2 5/4/06 9:30 AM Page 47 ADDING INTEGERS Case 4: One of the numbers is zero. Painless Solution: Zero plus any number is that number. EXAMPLES: (ϩ2) ϩ 0 ϭ ϩ2 0 ϩ (Ϫ8) ϭ Ϫ8 Visual Clue: Use a number line to help in adding integers.

24 algebra_ch1 5/4/06 9:27 AM Page 25 PROPERTIES OF NUMBERS The Commutative Property of Multiplication The Commutative Property of Multiplication states that, no matter in what order you multiply two numbers, the answer is always the same. Written in Math Talk, the Commutative Property of Multiplication is a(b) ϭ b(a). Given any two numbers, a and b, a times b is equal to b times a. EXAMPLES: 3 и 5 ϭ 5 и 3 because 15 ϭ 15. 6(1) ϭ 1(6) because 6 ϭ 6. ᎏ1ᎏ(4) 2 ϭ 4 ᎏ21ᎏ because 2 ϭ 2. Caution—Major Mistake Territory!

Today’s low was five degrees below zero. Tonight the temperature is expected to drop to negative twelve degrees. algebra_ch2 5/4/06 9:30 AM Page 36 algebra_ch2 5/4/06 9:30 AM Page 37 CT HEAD The weather forecaster for the preceding report used negative numbers to express how cold it was outside, because the temperature was below zero. When you first learned to count, you counted with positive numbers, the numbers greater than zero: 1, 2, 3, 4, 5. That’s why these numbers are called the counting numbers.

### SGA 6: Theorie des reductions et theoreme de Riemann-Roch by A. Grothendieck

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