PDF 
Paper 
Description 
Found in 
Fixed in 
4 

#52334: Page 4 of preview chapter irrationals.pdf:
"According to legeng" > legend
Page 5
"...consists of a string of 0s and 1s where for digit x, 10^x is a 1 if and only if there is some integer n such that n! = i."
Shouldn't that be 'x! = i'? n is not defined previous to its use in the condition; x is not used in the condition.Istvan Kovacs #52334: Page 4 of preview chapter irrationals.pdf:
"According to legeng" > legend
Page 5
"...consists of a string of 0s and 1s where for digit x ...more...

P1.0
07Aug13


5 

#52303: The subset statement
N_2 [subset] N
(Section "Cantor's diagonalization"; I'm reading
the sample pages, so I cannot give a page number)
should be
[ForAll] x: IsEvenNatural(x) => IsNatural(x)
not
[ForAll] x: IsEvenNatural(x) <=> IsNatural(x)Christian Heinze #52303: The subset statement
N_2 [subset] N
(Section "Cantor's diagonalization"; I'm reading
the sample pages, so I cannot give a page number)
...more...

B1.0
02Aug13


6 

#52336: Page 6 of preview chapter irrationals.pdf
"Since the value of e^(i*pi) is not transcendental — it’s 1 — then pi must be transcendental."
The value of e^(i*pi) is 1, not 1.Istvan Kovacs #52336: Page 6 of preview chapter irrationals.pdf
"Since the value of e^(i*pi) is not transcendental — it’s 1 — then pi must be transcendental."
T ...more...

P1.0
07Aug13


7 

#52059: At the bottom of the page, in step 1, below 'So we can substitute that in and get this:' it should be after the equal sign: (n + 1)(n + 2) / 2 instead of (n + 1)(n + 2) / n [denominator 2 instead of n]Christian Raeber #52059: At the bottom of the page, in step 1, below 'So we can substitute that in and get this:' it should be after the equal sign: (n + 1)(n + 2) / 2 ...more...

B6.0
24Jun13


7q 

#52333: States:
n(n+1) (n+1)(n+2)
 + n + 1 = 
2 n
should be:
n(n+1) (n+1)(n+2)
 + n + 1 = 
2 2
#52333: States:
n(n+1) (n+1)(n+2)
 + n + 1 = 
2 n
should be:
n(n+1) (n+1)(n+2)
 ...more...

P1.0
07Aug13


7 

#52339: In the equation on the bottom of the page, under "So we can substitute that in and get this:" shouldn't the right hand denominator be a 2 rather then a n? (Or I could be really missing something....)Ned Wolpert #52339: In the equation on the bottom of the page, under "So we can substitute that in and get this:" shouldn't the right hand denominator be a 2 rath ...more...

P1.0
07Aug13


7 

#58790: Peano induction rule proof for "Summation of N+1 natural numbers", the error is on the last line of the page on the right hand side divided by "n" is printed instead of 2.Suneel #58790: Peano induction rule proof for "Summation of N+1 natural numbers", the error is on the last line of the page on the right hand side divided by ...more...

P1.0
03Jan14


7 

#52417: Bottom of page
n(n + 1)/2 + n + 1 = (n + 1)(n + 2) / n
shouldn't that be
n(n + 1)/2 + n + 1 = (n + 1)(n + 2) / 2
Philip Martel

P1.0
18Aug13


7 

#52476: In the right side of last formula in Chapter 1 p.7 the denominator of the fraction should be 2 instead of n.

P1.0
27Aug13


10 

#52337: Page 10 of cantor.pdf
[...] D(x,y) returns the yth digit of the decimal expansion of R(x)
[...]
D(x,3) is the third digit of the binary expansion of x.
'binary' > should be 'decimal'Istvan Kovacs #52337: Page 10 of cantor.pdf
[...] D(x,y) returns the yth digit of the decimal expansion of R(x)
[...]
D(x,3) is the third digit of the binary exp ...more...

P1.0
07Aug13


12 
xii 
#52345: There are two nearly identical sentences on this page:
"I figured that I’d probably get a couple of dozen people to read it and that I’d probably give up on it after a couple of weeks."
"I thought that I’d probably be read by a couple dozen people, and I’d give up in disgust after a couple of weeks."
Reading it the second time was jarring and disrupted the flow of the book. I did a doubletake, wondering if my eyes had jumped around the page accidentally.David Bock #52345: There are two nearly identical sentences on this page:
"I figured that I’d probably get a couple of dozen people to read it and that I’d pr ...more...

P1.0
08Aug13


13 

#53268: This doesn't seem correct to me:
The definition of subtraction turns out to be pretty neat. 3–5 would be (3,0)–(5,0),which is equal to (3,0)+(0,5)=(3,5), which is an element of the equivalence class of –2.
Shouldn't this be:
The definition of subtraction turns out to be pretty neat. 3–5 would be (0,3)–(0,5),which is equal to (0,3)+(5,0)=(5,3), which is an element of the equivalence class of –2. #53268: This doesn't seem correct to me:
The definition of subtraction turns out to be pretty neat. 3–5 would be (3,0)–(5,0),which is equal to (3,0 ...more...

P1.0
03Dec13


15 

#52583: Bit of a nitpick but...
The third paragraph starts as follows "There are a couple of ways to describe the real numbers. I’m going to take you through three of them" which feels a bit like Douglas Adams' "trilogy in four parts"
(Now experiencing mild paranoia that I've missed a brilliant mathematical joke.)Liz Conlan #52583: Bit of a nitpick but...
The third paragraph starts as follows "There are a couple of ways to describe the real numbers. I’m going to take y ...more...

P1.0
05Sep13



18+19 
#76456: The field axioms are already valid for the rational numbers, and the ordering as well. Both are not specific for the real numbers. Really new is only the continuity. If the real numbers are defined as the set of limits (as far as they exist) of sequences of rational numbers, it can be proven that the arithmetic operations are continuous and are therefore also defined in the real numbers.Dr. Gerhard Nehmiz #76456: The field axioms are already valid for the rational numbers, and the ordering as well. Both are not specific for the real numbers. Really new ...more...

P1.0
28Feb14



20 
#53117: (My book version reads "P1.0July 2013" and as such is not listed on the erratum entry page under "Version of Book With Error".)
Shouldn't the 4th line read
"3. if x <= y, then for all z <= 0, (y * z) <= (x * z)"
instead of
"3. if x <= y, then for all z <= 0, (x * z) <= (y * z)"
?Werner Wenzel #53117: (My book version reads "P1.0July 2013" and as such is not listed on the erratum entry page under "Version of Book With Error".)
Shouldn't ...more...

P1.0
06Nov13


20 
6 
#52352: This was confusing to me:
Recursion For any natural numbers m and n,
m + s(n) = s(m + n)
...
It’s easier to read if you just rewrite it a tad to use +1 and –1:
m + n = 1 + (m + (n – 1))
I didn't understand why this:
m + s(n)
...was represented as:
m + n
...instead of:
m + (1 + n)
And why this:
s(m + n)
...was represented as:
1 + (m + (n – 1))
...instead of:
1 + (m + n)
It seems to ignore the successor rule from the LHS, add the predecessor rule to the RHS. #52352: This was confusing to me:
Recursion For any natural numbers m and n,
m + s(n) = s(m + n)
...
It’s easier to read if you just rewrite ...more...

P1.0
09Aug13


20 

#52453: The 3th point of:
• “≤” is compatible with “+” and “×”:
1. If x ≤ y then (x + 1) ≤ (y + 1).
2. If x ≤ y, then for all z where 0 ≤ z, (x × z) ≤ (y × z).
3. If x ≤ y, then for all z ≤ 0, (x × z) ≤ (y × z).
looks not correct for me!
ex. x = 1, y = 2, z = 1 then (1 x 1) > ( 2 x 1).
johan.neven@gmail.com #52453: The 3th point of:
• “≤” is compatible with “+” and “×”:
1. If x ≤ y then (x + 1) ≤ (y + 1).
2. If x ≤ y, then for all z where 0 ≤ z, (x × ...more...

P1.0
25Aug13


21 

#53094: the last equation on that page has the right hand side with a denominator of 'n', whereas I believe it should be '2'. Otherwise the rest of the proof makes no sense to me. #53094: the last equation on that page has the right hand side with a denominator of 'n', whereas I believe it should be '2'. Otherwise the rest of th ...more...

P1.0
30Oct13



24 
#76457: A small omission: "There's no finite sequence of ... and roots _with only integer numbers_ that will give you the value of a transcendental number."Dr. Gerhard Nehmiz

P1.0
28Feb14


50 

#52419: The description of electrical power is wrong. The power does turn on and off. If you apply AC to a resistive load, you can detect the change in power as a change in heat produced. The output of a small incandescent bulb can be read with a photosensor and will be seen to vary.
If you reduce the frequency of the AC the effect becomes easier to detect.Philip Martel #52419: The description of electrical power is wrong. The power does turn on and off. If you apply AC to a resistive load, you can detect the change ...more...

P1.0
19Aug13



72 
#53143: (My book version reads "P1.0July 2013" and as such is not listed on the erratum entry page under "Version of Book With Error".)
Shouldn't the 2nd line of the last paragraph immediately before "Cleaner, Clearer, and Just Plain Fun" read
"1/(1+1/(1+1/(3+1/2))), or [0; 1, 1, 3, 2]."
instead of
"1/(1+1/(1+3/(1+1/2))), or [0; 1, 1, 3, 2]."
?Werner Wenzel #53143: (My book version reads "P1.0July 2013" and as such is not listed on the erratum entry page under "Version of Book With Error".)
Shouldn't ...more...

P1.0
12Nov13



72 
#53148: (My book version reads "P1.0July 2013" and as such is not listed on the erratum entry page under "Version of Book With Error".)
Shouldn't lines 4  6 in the 2nd paragraph after "Cleaner, Clearer, and Just Plain Fun" read
"... Take a number like 2.3456, aka [2; 2, 1, 8, 2, 1, 1, 4]. The reciprocal is [0; 2, 2, 1, 8, 2, 1, 1, 4]. ..."
instead of
"... Take a number like 2.3456, aka [2; 2, 3, 1, 3, 4, 5, 6, 4]. The reciprocal is [0; 2, 2, 3, 1, 3, 4, 5, 6, 4]. ..."
?Werner Wenzel #53148: (My book version reads "P1.0July 2013" and as such is not listed on the erratum entry page under "Version of Book With Error".)
Shouldn't ...more...

P1.0
13Nov13



73 
#58777: Since PI = 3.141592653589793..., a more accurate statement would be that our continued fraction is accurate to 9 decimal places, not 11.Heinz Kabutz

P1.0
30Dec13


73 

#52418: "Adding a single convergent to a continuedfraction approximation adds more information than adding a single digit."
Not always true. The author's "favorite" number, Phi, is a good counterexample. It takes 11 convergents to get the 4th decimal digit and 23 to get the 9th decimal digitPhilip Martel #52418: "Adding a single convergent to a continuedfraction approximation adds more information than adding a single digit."
Not always true. The a ...more...

P1.0
18Aug13


95 

#52944: In the explanation of Step 2, you used the "Or negation" rule, not "And negation". Also in the table of rules you have two labeled "Or Negation" one on page 93 and one on 94. #52944: In the explanation of Step 2, you used the "Or negation" rule, not "And negation". Also in the table of rules you have two labeled "Or Negatio ...more...

P1.0
17Sep13


99 

#52467: In figure 1, the first line of the truth tree has (sorry, I can't copy the symbols)
not((A impl B) and (B impl C)) impl (A impl C)
To be the contradiction of
((A impl B) and (B impl C)) impl (A impl C)
Shouldn't the line be
not((A impl B) and (B impl C) impl (A impl C)) ?
Philip Martel #52467: In figure 1, the first line of the truth tree has (sorry, I can't copy the symbols)
not((A impl B) and (B impl C)) impl (A impl C)
To be t ...more...

P1.0
26Aug13



130 
#53269: The symbol you're using for equivalence in the definition of set union and subsequently throughout the book looks wrong. It's used consistently throughout, but it isn't formally introduced and I have always been taught that the equivalence symbol is three parallel horizontal lines.Piers Cawley #53269: The symbol you're using for equivalence in the definition of set union and subsequently throughout the book looks wrong. It's used consistentl ...more...

P1.0
03Dec13


131 

#52468: So Parent is a subset of the values from the
Cartesian product of the set of people with itself. (Mark,
Rebecca) ∈ Parent, and Parent is a predicate on the set
Parent × Parent
Should be: "Parent is a predicate on the set of Person × Person" Philip Martel #52468: So Parent is a subset of the values from the
Cartesian product of the set of people with itself. (Mark,
Rebecca) ∈ Parent, and Parent is a p ...more...

P1.0
26Aug13


140 

#52475: The Axiom of Extensionality
∀ A, B : A = B ≨ (∀ C : C ∈ A ⇒ C ∈ B)
This is a formal way of saying that a set is described by
its members: two sets are equivalent if and only if they
contain the same members.
I'm not positive, but that looks more like the definition of "A is a subset of B". Don't you have to have
((∀ C : C ∈ A ⇒ C ∈ B)∧(∀ D : D ∈ B ⇒ D ∈ A)) ?Philip Martel #52475: The Axiom of Extensionality
∀ A, B : A = B ≨ (∀ C : C ∈ A ⇒ C ∈ B)
This is a formal way of saying that a set is described by
its members: t ...more...

P1.0
27Aug13


141 

#52532: but we had no way of creating a set containing
both the empty set and the set containing the empty set
({∅, {∅}).
Missing '}' before ')'.Philip Martel

P1.0
31Aug13


142 

#52533: Axiom of infinity
∃ N : ∅ ∈ N ∧ (∀ x : x ∈ N ⇒ x ∪ { x } ∈ N)
It's probably ok as written, but since you haven't specified an operator precedence something like
∃ N : ∅ ∈ N ∧ (∀ x : x ∈ N ⇒ {x ∪ { x }} ∈ N)
would be clearer.Philip Martel #52533: Axiom of infinity
∃ N : ∅ ∈ N ∧ (∀ x : x ∈ N ⇒ x ∪ { x } ∈ N)
It's probably ok as written, but since you haven't specified an operator pre ...more...

P1.0
31Aug13


148 

#52531: But it implies something absolutely crazy: the wellordering
theorem says that there’s a single, unique value that is the
smallest positive real number larger!
larger than what??Philip Martel #52531: But it implies something absolutely crazy: the wellordering
theorem says that there’s a single, unique value that is the
smallest positive ...more...

P1.0
31Aug13


157 

#52534: The natural number 0 will represent the integer 0; 0 is
even, because 0 * 0 = 0; so 0 is represented by the empty
set.
That should be "0 is even, because 2 * 0 = 0"Philip Martel #52534: The natural number 0 will represent the integer 0; 0 is
even, because 0 * 0 = 0; so 0 is represented by the empty
set.
That should be "0 is ...more...

P1.0
31Aug13


163 
154 
#52053: "that is the smallest positive number larger!" doesn't make sense. The last sentence of the paragraph makes the point that this sentence does not. Mitch Amiano

B6.0
23Jun13



168 
#58771: in table 3, the cell at row g column d
should be "g" if d = 0
there's also a "1" in (j,b)

P1.0
28Dec13


185 

#52547: I'm torn between "Typo" and "Technical Error" here
"For example, we can create a machine that accepts strings
that consist of any string containing at least one a, followed by at least one b."
then you go on showing examples with "baab" being a string that is not accepted. "baab" *IS* a string containing at least one 'a' followed by at least one 'b'.
I know what you mean, but it's not what you said.Philip Martel #52547: I'm torn between "Typo" and "Technical Error" here
"For example, we can create a machine that accepts strings
that consist of any string con ...more...

P1.0
01Sep13


186 

#52551: Figure 15 shows state A marked as final. This means that your machine would accept the string "a", which is *not*
an element of the set of "strings that consist of any string containing at least one a, followed by at least one b."
This error also shows up on P.194 item 5.b
Philip Martel #52551: Figure 15 shows state A marked as final. This means that your machine would accept the string "a", which is *not*
an element of the set of " ...more...

P1.0
01Sep13


190 

#52548: "all of the different FSMs that
you can generate for a particular regular expression will
process exactly the same language and will do it in exactly
the same amount of time."
You don't mention "time" anywhere else in the chapter in the sense of an amount of time. Please either expand on what you mean or delete the sentence.Philip Martel #52548: "all of the different FSMs that
you can generate for a particular regular expression will
process exactly the same language and will do it i ...more...

P1.0
01Sep13


190 

#52549: In formal terms, let S(r) be the set of strings accepted by the
regular expression r. Then if you have a regular expression
r and a character c, the derivative of r with respect to c
(written Dc(r)) is a regular expression r’ such that t ∈ S(r’) if
and only if ct ∈ S(r).
For example, if you had a regular expression ab*, then the
derivative with respect to a would be ab*.
That derivative would be b*, not ab*
Philip Martel #52549: In formal terms, let S(r) be the set of strings accepted by the
regular expression r. Then if you have a regular expression
r and a characte ...more...

P1.0
01Sep13


192 

#52550: A starred regular expression matches zero or one repetitions
of a pattern. Zero repetitions is the empty string,
so any starred regular expression can match the empty
string.
Should be A starred regular expression matches zero or more repetitions...Philip Martel #52550: A starred regular expression matches zero or one repetitions
of a pattern. Zero repetitions is the empty string,
so any starred regular expr ...more...

P1.0
01Sep13



202 
#58368: The last state in the list should not contain the minus, since the transition eraseone minus writes space.Heinz Kabutz

P1.0
27Dec13



206 
#58778: The link for the Turing Machine written in Haskell points to the website for the book, but the source code zip does not include the TM simulation.Heinz Kabutz

P1.0
30Dec13


238 

#52630: The factorial function N! is defined for all natural numbers: for any natural number N, its factorial is the product of all of the integers less than or equal to N.
You are entitled to define N! any way you want, but with that definition, the "Well almost" at the bottom of the page is the way it is. No N! calculation will ever terminate.
You can avoid this by saying "The factorial function N! is defined for all natural numbers: for any natural number N, its factorial is the product of all of the *natural numbers*
less than or equal to N." Then the only issue is defining 0!, which you should probably do by saying explicitly 0! = 1
Philip Martel #52630: The factorial function N! is defined for all natural numbers: for any natural number N, its factorial is the product of all of the integers le ...more...

P1.0
13Sep13


238 

#52633: Please amend my earlier post to say
"The factorial function N! is defined for all natural numbers: for any natural number N, its factorial is the product of all of the *natural numbers > 0*
less than or equal to N"Philip Martel #52633: Please amend my earlier post to say
"The factorial function N! is defined for all natural numbers: for any natural number N, its factorial i ...more...

P1.0
13Sep13


245 

#52631: The λ which is the very last character should really be on the next page. Philip Martel

P1.0
13Sep13


246 

#52632: The context is usually written as an
uppercase letter. If a type context G includes the judgement
that x : γ, we’ll write that as G : x : γ”.
For the simply typed λ calculus, a simplified version of the
type inference rules are given here:
Type Identity
(overbar)
x : α ⊧ x : α
First, is the symbol ” in G : x : γ”. part of the "judgement", or is there a missing " before the G?
Next, you use : in G : x : γ” but for the rest of the discussion it looks like you are using the symbol ⊧Philip Martel #52632: The context is usually written as an
uppercase letter. If a type context G includes the judgement
that x : γ, we’ll write that as G : x : γ ...more...

P1.0
13Sep13



248 
#52099: Last line substitute 'δ' by 'β' or on the 2nd line of page 249 the other way round:
implication isn’t accidental: a function type α → δ is a logical
should be:
implication isn’t accidental: a function type α → β is a logicalDr. Frid Ruland #52099: Last line substitute 'δ' by 'β' or on the 2nd line of page 249 the other way round:
implication isn’t accidental: a function type α → δ is a ...more...

B7.0
30Jun13


257 

#52634: "And finally, the way that
we would write that a program p doesn’t halt for input i is
C(p, i) = _."
You should probably use the "⊥" you use in the description of the halting oracle at the bottom of the page.
Philip Martel #52634: "And finally, the way that
we would write that a program p doesn’t halt for input i is
C(p, i) = _."
You should probably use the "⊥" you ...more...

P1.0
13Sep13

