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Sep 1 In-Class Exercise.

Please post your solution to the Sep 1 In-Class Exercise to this thread.

Best,

Chris

Please post your solution to the Sep 1 In-Class Exercise to this thread. Best, Chris

-- Sep 1 In-Class Exercise

integer→ (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* 
 
number→ real
real→ integer exponent
integer→ 1
exponent→ E-integer
integer→ 4
therefore, number→ 1E-4

(Edited: 2021-09-01)

<pre> integer→ (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* number→ real real→ integer exponent integer→ 1 exponent→ E-integer integer→ 4 therefore, number→ 1E-4 </pre>

-- Sep 1 In-Class Exercise

integer -> (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)*

a number can be a real. a real can be an integer (in this case 1) followed by an exponent. an exponent is e or E (in this case E) followed by +, -, or ε, (in this case -) followed by an integer. an integer is a digit (in this case 4) followed by 0 or more digits (none in this case)

(Edited: 2021-09-01)

integer -> (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* a number can be a real. a real can be an integer (in this case 1) followed by an exponent. an exponent is e or E (in this case E) followed by +, -, or ε, (in this case -) followed by an integer. an integer is a digit (in this case 4) followed by 0 or more digits (none in this case)

-- Sep 1 In-Class Exercise

integer→ (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)*

A number is real. A real is an integer. An integer can be followed by an exponent. 1 is an integer. 1 is followed by E-4, which is the exponent. As a result, 1E-4 is a number.

(Edited: 2021-09-01)

integer→ (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* A number is real. A real is an integer. An integer can be followed by an exponent. 1 is an integer. 1 is followed by E-4, which is the exponent. As a result, 1E-4 is a number.

-- Sep 1 In-Class Exercise

The regular expression definition of a number is integer|real An integer is (0|1|2|3|4|5|6|7|8|9)* 1 is an integer, An integer is a digit, E-4 is an exponent, An exponent is a integer, Therefore 1E-4 is a number

(Edited: 2021-09-01)

The regular expression definition of a number is integer|real An integer is (0|1|2|3|4|5|6|7|8|9)* 1 is an integer, An integer is a digit, E-4 is an exponent, An exponent is a integer, Therefore 1E-4 is a number

-- Sep 1 In-Class Exercise

integer -> (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* 
 
number -> real
real -> integer exponent
integer -> 1
exponent -> 4 
 
making 1E-4 a number

(Edited: 2021-09-01)

<pre> integer -> (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* number -> real real -> integer exponent integer -> 1 exponent -> 4 making 1E-4 a number </pre>

-- Sep 1 In-Class Exercise

integer --> digit digit*
digit --> 0|1|2|3|4|5|6|7|8|9
integer --> (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* 
 
number --> integer|real
real --> integer exponent|decimal(exponent|empty string)
exponent --> (e|E)(+|-|empty string)integer 
 
1E-4 is a number. Because it has "E" in it, it does not match the regular expression for integer, so it must be a real.
1 matches the first integer.
Because there is no decimal, E-4 must match the exponent regular expression.
E matches e or E.
- matches +, -, or empty string
4 matches integer, so E-4 matches the exponent regular expression.
The string ends, so empty string matches exponent or empty string.
So 1E-4 matches the regular expression for a real, which means it also matches the regular expression for a number.

(Edited: 2021-09-01)

<pre> integer --> digit digit* digit --> 0|1|2|3|4|5|6|7|8|9 integer --> (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* number --> integer|real real --> integer exponent|decimal(exponent|empty string) exponent --> (e|E)(+|-|empty string)integer 1E-4 is a number. Because it has "E" in it, it does not match the regular expression for integer, so it must be a real. 1 matches the first integer. Because there is no decimal, E-4 must match the exponent regular expression. E matches e or E. - matches +, -, or empty string 4 matches integer, so E-4 matches the exponent regular expression. The string ends, so empty string matches exponent or empty string. So 1E-4 matches the regular expression for a real, which means it also matches the regular expression for a number. </pre>

-- Sep 1 In-Class Exercise

integer expanded: (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)*

1E-4: 1->integer|real E-> exponent | integer '-'-> exponent 4 -> digit

			Therefore 1E-4 is a number

(Edited: 2021-09-01)

integer expanded: (0|1|2|3|4|5|6|7|8|9)(0|1|2|3|4|5|6|7|8|9)* 1E-4: 1->integer|real E-> exponent | integer '-'-> exponent 4 -> digit Therefore 1E-4 is a number

-- Sep 1 In-Class Exercise

1 is digit

Since decimal -> digit *(.digit|digit) digit*

Exponent -> (e|E)(+|-|e)integer

Then E- 4 is exponent

Since number -> interger exponent|decimal(exponent|e)

Then 1E-4 is number

(Edited: 2021-09-01)

-- Sep 1 In-Class Exercise

1. integer --> (digit --> (0|1|2|3|4|5|6|7|8|9) digit*)
2. a real is an integer followed by an exponent OR a decimal followed by an exponent OR
 the empty set. Therefore the literal 1E-4 is an integer 1 followed by the exponent E-4 as
 defined by the exponent rule exponent --> (e|E)(+|-|"")integer. we know 4 is an integer 
 as it a digit 4 followed by 0 or more digits thus completing the exponent rule. therefore 
 1E-4 is a real by integer exponent definition therefore it is a number as a number--> integer|real

(Edited: 2021-09-01)

<pre> 1. integer --> (digit --> (0|1|2|3|4|5|6|7|8|9) digit*) 2. a real is an integer followed by an exponent OR a decimal followed by an exponent OR the empty set. Therefore the literal 1E-4 is an integer 1 followed by the exponent E-4 as defined by the exponent rule exponent --> (e|E)(+|-|"")integer. we know 4 is an integer as it a digit 4 followed by 0 or more digits thus completing the exponent rule. therefore 1E-4 is a real by integer exponent definition therefore it is a number as a number--> integer|real </pre>