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| showing the truth or falsehood of a given statement by a straightforward combination of established facts |
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Claim: P(n) is true for all positive integers n.
Proof: We’ll use induction on n.
Base: We need to show that P(1) is true.
Induction: Suppose that P(n) is true for n = 1, 2, . . . , k−1. We
need to show that P(k) is true. |
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Definition
| Every element is related to itself |
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| No element is related to itself |
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Definition
a is related to b if b is related to a.
for all x, y ∈ A, xRy implies yRx
Ex:
if 3 -> 4 then 4 -> 3 (related backwards/forwards) |
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| A function is equivalent if |
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Definition
| type signature and output are the same. |
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| ∀x, y ∈ A, x != y → f(x) != f(y) |
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| Every variable is defined by 4 properties |
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Definition
| Type, Name, value, memory location |
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| Separates methods from methods, represented as a pill and as .h/.cpp files in c++ |
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| Things to include and where in c++ files |
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Definition
#pragma once - top of .h file
#include "Cube.h" - top of .cpp file |
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| Large libraries in C++ are organized into |
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| Constructors in C++, defined where? |
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| Top of public h file, defined as Cube.h for example. |
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| &c -> returns the memory address of c's data |
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Definition
| returns the data at that memory address |
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| What should we never do with stack memory? |
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| Return a pointer to the stack variable |
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| All 3: Reflexive, symmetric, transitive. |
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