Summary: Introduction To Computer Science
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Read the summary and the most important questions on Introduction to Computer Science
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1 Introduction to Computer Science
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What is the definition of the natural numbers (\(N_0\))?
- \(N_0 = \{0\} \cup \mathbb{N}\)
- \(\mathbb{N} = \{0, 1, 2, 3, \ldots\}\)
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What are the properties of multiplication for natural numbers?
- With neutral element 1
- \(1 \cdot a = a\)
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Describe the commutative property of addition for natural numbers.
- \(a + b = b + a\)
- For all \(a, b \in \mathbb{N}\)
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Describe the associative property of multiplication for natural numbers.
- \(a \cdot (b \cdot c) = (a \cdot b) \cdot c\)
- For all \(a, b, c \in \mathbb{N}\)
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Describe the associative property of addition for natural numbers.
- \(a + (b + c) = (a + b) + c\)
- For all \(a, b, c \in \mathbb{N}\)
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Describe the distributive property over addition for natural numbers.
- \(a \cdot (b + c) = a \cdot b + a \cdot c\)
- For all \(a, b, c \in \mathbb{N}\)
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What defines the inverse of a natural number under addition?
- Integer \(a \in \mathbb{Z} \setminus \{0\} \cup \mathbb{N}\)
- Object that satisfies \(a + (-a) = 0\)
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What defines the inverse of a natural number under multiplication?
- Integer \(a \in \mathbb{Z} \setminus \{0\}\)
- Object that satisfies \(a \cdot a^{-1} = 1\)
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How are integers (\(Z\)) defined?
- \(\mathbb{Z} = -\mathbb{N} \cup \{0\} \cup \mathbb{N}\) -
How are rational numbers (\(\mathbb{Q}\)) defined?
- \(\mathbb{Q} = \frac{z1}{z2}\)
- \(z1, z2 \in \mathbb{Z} \setminus \{0\}\)
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