Scope of formula - Revision history

Riegler: Riegler moved page DecodingWork:Scope of formula to Scope of formula: abandoning DecodingWork-namespce

2024-07-22T14:30:29Z

Riegler moved page DecodingWork:Scope of formula to Scope of formula: abandoning DecodingWork-namespce

← Older revision

Revision as of 16:30, 22 July 2024

Riegler: typo

2024-07-22T14:22:18Z

typo

← Older revision		Revision as of 16:22, 22 July 2024
Line 7:		Line 7:
	==Examples==		==Examples==

	#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2</math> and, hence, does not equal <math>a=2</math>.		#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2</math> and, hence, does not equal <math>a=-2</math>.
	#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]		#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler at 12:32, 22 July 2024

2024-07-22T12:32:24Z

← Older revision		Revision as of 14:32, 22 July 2024
Line 8:		Line 8:

	#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2</math> and, hence, does not equal <math>a=2</math>.		#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2</math> and, hence, does not equal <math>a=2</math>.

	#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]		#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler: typo

2024-07-22T12:31:57Z

typo

← Older revision		Revision as of 14:31, 22 July 2024
Line 7:		Line 7:
	==Examples==		==Examples==

	#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2 and, hence, does not equal <math>a=2</math>.		#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2</math> and, hence, does not equal <math>a=2</math>.

	#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]		#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]

Riegler: extended example

2024-07-22T12:31:27Z

extended example

← Older revision		Revision as of 14:31, 22 July 2024
Line 7:		Line 7:
	==Examples==		==Examples==

	#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite.		#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite. Of course, the fomula then leads to wrong results if the ignored prerequisite does not hold. This is e.g. the case for <math>a=-2</math>. There <math>\sqrt{a^2}=\sqrt{(-2)^2}=\sqrt{4}=2 and, hence, does not equal <math>a=2</math>.

	#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]		#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler at 12:09, 22 July 2024

2024-07-22T12:09:15Z

← Older revision		Revision as of 14:09, 22 July 2024
Line 7:		Line 7:
	==Examples==		==Examples==

	#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of ~~prerequisites~~.		#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of this prerequisite.
	#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]		#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler at 08:08, 22 July 2024

2024-07-22T08:08:57Z

← Older revision		Revision as of 10:08, 22 July 2024
Line 7:		Line 7:
	==Examples==		==Examples==

	# Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>.		#Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>. In fact, many students use <math>\sqrt{a^2}=a</math> without checking the applicability/validity of prerequisites.
	# Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]		#Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler: +examples

2024-07-22T08:07:49Z

+examples

← Older revision		Revision as of 10:07, 22 July 2024
Line 6:		Line 6:

	==Examples==		==Examples==
	~~<br />~~

	==~~See also==~~		# Square root and square are inverse to each other for nonnegative real numbers, i.e. for <math>a \ge 0</math>: <math>\sqrt{a^2}=a</math>. Without the prerequisite <math>a \ge 0</math> the formula would read <math>\sqrt{a^2}=\|a\|</math>.
			# Scope of quadratic formula as described in [[DecodingWork:Scope of quadratic formula]]
	*[[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler: /* Example */

2024-07-22T07:59:42Z

Example

← Older revision		Revision as of 09:59, 22 July 2024
Line 5:		Line 5:
	This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation.		This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation.

	==~~Example~~==		==Examples==
	<br />		<br />

	== See also ==		==See also==

	* [[DecodingWork:Scope of quadratic formula]]		*[[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]

Riegler: + see also

2024-07-17T14:14:19Z

+ see also

← Older revision		Revision as of 16:14, 17 July 2024
Line 5:		Line 5:
	This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation.		This bottleneck relates to the following intended learning outcome: Students always check whether a given formula comes with prerequisites for its applicability and whether these prerequisites hold in a given situation.

	== Example ==		==Example==
	<br />		<br />

			== See also ==

			* [[DecodingWork:Scope of quadratic formula]]

	[[Category:Mathematics]]		[[Category:Mathematics]]
	[[Category:Bottleneck]]		[[Category:Bottleneck]]