Proofs:Cases - Revision history

Lila: /* Resoucres */

2021-09-24T16:50:31Z

Resoucres

Lila at 16:48, 24 September 2021

2021-09-24T16:48:31Z

Lila: Created page with "Some proofs are easier to do if we split them up into two or more cases. Example: Proof that $x^2 \ge 0$ for all real numbers. We can break this up into three ca..."

2021-09-24T16:47:35Z

Created page with "Some proofs are easier to do if we split them up into two or more cases. Example: Proof that <math> x^2 \ge 0 </math> for all real numbers. We can break this up into three ca..."

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Some proofs are easier to do if we split them up into two or more cases.

Example: Proof that <math> x^2 \ge 0 </math> for all real numbers. We can break this up into three cases: <math> x^2 \ge 0 </math>, <math> x = 0 </math>, and <math> x < 0 </math>. If <math> x > 0 </math>, then <math> x^2 = x*x \ge 0 </math>, since the product of two positive numbers is positive. If <math> x = 0 </math>, then <math> x^2 = 0*0 = 0 </math>. If <math> x < 0 </math>, then <math> x^2 = x*x </math> is the product of two negative numbers, which is positive. Thus, <math> x^2 \ge 0 </math> for all three cases, and is therefore true for all real numbers x.

Examples of other ways to break sets into cases:
* Integers: "z is negative" and "z is nonnegative", "z is even" and "z is odd", etc.
* Real numbers: "x is rational" and "x is irrational", "<math> x < 7 </math>" and "<math> x \ge 7 </math>", "<math> |x| \le 1 </math>" and "<math> "<math> |x| > 1 </math>" and "<math> x \ge 7 </math>" </math>", etc.

==Resoucres==
* [https://sites.millersville.edu/bikenaga/math-proof/proof-by-cases/proof-by-cases.html Proof by Cases], Millersville University

@@ Line 7: / Line 7: @@
 * Real numbers: "x is rational" and "x is irrational", "<math> x < 7 </math>" and "<math> x \ge 7 </math>", "<math> |x| \le 1 </math>" and "<math> |x| > 1 </math>" and "<math> x \ge 7 </math>" </math>", etc.
-==Resoucres==
+==Resources==
 * [https://sites.millersville.edu/bikenaga/math-proof/proof-by-cases/proof-by-cases.html Proof by Cases], Millersville University

@@ Line 5: / Line 5: @@
 Examples of other ways to break sets into cases:
 * Integers: "z is negative" and "z is nonnegative", "z is even" and "z is odd", etc.
-* Real numbers: "x is rational" and "x is irrational", "<math> x < 7 </math>" and "<math> x \ge 7 </math>", "<math> |x| \le 1 </math>" and "<math> "<math> |x| > 1 </math>" and "<math> x \ge 7 </math>" </math>", etc.
+* Real numbers: "x is rational" and "x is irrational", "<math> x < 7 </math>" and "<math> x \ge 7 </math>", "<math> |x| \le 1 </math>" and "<math> |x| > 1 </math>" and "<math> x \ge 7 </math>" </math>", etc.
 ==Resoucres==
 * [https://sites.millersville.edu/bikenaga/math-proof/proof-by-cases/proof-by-cases.html Proof by Cases], Millersville University

Proofs:Cases - Revision history

Lila: /* Resoucres */

Lila at 16:48, 24 September 2021

Lila: Created page with "Some proofs are easier to do if we split them up into two or more cases. Example: Proof that x^2 \ge 0 for all real numbers. We can break this up into three ca..."

Lila: Created page with "Some proofs are easier to do if we split them up into two or more cases. Example: Proof that $x^2 \ge 0$ for all real numbers. We can break this up into three ca..."