Originally posted by NotAllThere
View Post
- Visitors can check out the Forum FAQ by clicking this link. You have to register before you can post: click the REGISTER link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below. View our Forum Privacy Policy.
- Want to receive the latest contracting news and advice straight to your inbox? Sign up to the ContractorUK newsletter here. Every sign up will also be entered into a draw to WIN £100 Amazon vouchers!
Antisemitism in Christianity
Collapse
X
Collapse
-
"Don't part with your illusions; when they are gone you may still exist, but you have ceased to live" Mark Twain -
Originally posted by Cirrus View PostSorry: typo. I meant 1+1=2 is defined as a part of integer arithmetic. You don't need to prove it or use statistics etc. It is by definition true.
But it isn't a tautology. It's a proposition.
Alfred North Whitehead and Bertrand Russell spent a couple of hundred pages proving it in Principia Arithmetica. The Peano arithmetic proof of 1+1=2 arises from these axioms:
0 is a natural number.
The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.[5]
- For every natural number x, x = x. That is, equality is reflexive.
- For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
- For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
- For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.
- For every natural number n, S(n) is a natural number.
- For all natural numbers m and n, m = n if and only if S(m) = S(n). That is, S is an injection.
- For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Note: 1+1=2 is not an axiom. But it is provably true from these axioms. Of course, if you choose to define 2 as 1+1, then 1+1=2 is a tautology. But mathematicians don't define numbers like that.
Originally posted by TheGreenBastard View PostIn a different category of mathematics (statistics) what he's saying is true.
Originally posted by xoggoth View PostQuite. And if god is both good and almighty where did evil come from?
1. Why God (if existing) allows purposeless (non teleological) evil to exist?
2. Where does the notion of evil arise?
I got a 1st on my essay regarding the 1st in Philosophy at university. Though my main subject was maths. If you like we could argue about the number of angels who'll fit on the head of a pin.Down with racism. Long live miscegenation!Comment
-
Originally posted by NotAllThere View PostFor a start, even if it is a tautology, it in no way invalidates the contention that for a given x, 1+1=x has an infinitesimal probability of being true.
But it isn't a tautology. It's a proposition.
Alfred North Whitehead and Bertrand Russell spent a couple of hundred pages proving it in Principia Arithmetica. The Peano arithmetic proof of 1+1=2 arises from these axioms:
0 is a natural number.
The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.[5]
- For every natural number x, x = x. That is, equality is reflexive.
- For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
- For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
- For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.
- For every natural number n, S(n) is a natural number.
- For all natural numbers m and n, m = n if and only if S(m) = S(n). That is, S is an injection.
- For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Note: 1+1=2 is not an axiom. But it is provably true from these axioms. Of course, if you choose to define 2 as 1+1, then 1+1=2 is a tautology. But mathematicians don't define numbers like that.
It is a logical fallacy to say that because the probability of a proposition being true is infinitesimal, then the proposition isn't true.
Another interesting problem, discussed by minds greater than ours over the centuries. More interesting are these 2 questions.
1. Why God (if existing) allows purposeless (non teleological) evil to exist?
2. Where does the notion of evil arise?
I got a 1st on my essay regarding the 1st in Philosophy at university. Though my main subject was maths. If you like we could argue about the number of angels who'll fit on the head of a pin.
1 + 1 = II
1 + 1 + 1 + 1 = IV
1 + 1 + 1 + 1 + 1 = V
and V + V = X
and don't forget hexadecimal where A + B = 21
so, 2,3 4, etc are only character indicators which we find convenient and are taught to do maths in.Comment
-
Originally posted by NotAllThere View PostFor a start, even if it is a tautology, it in no way invalidates the contention that for a given x, 1+1=x has an infinitesimal probability of being true.
But it isn't a tautology. It's a proposition.
Alfred North Whitehead and Bertrand Russell spent a couple of hundred pages proving it in Principia Arithmetica. The Peano arithmetic proof of 1+1=2 arises from these axioms:
0 is a natural number.
The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.[5]
- For every natural number x, x = x. That is, equality is reflexive.
- For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
- For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
- For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.
- For every natural number n, S(n) is a natural number.
- For all natural numbers m and n, m = n if and only if S(m) = S(n). That is, S is an injection.
- For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Note: 1+1=2 is not an axiom. But it is provably true from these axioms. Of course, if you choose to define 2 as 1+1, then 1+1=2 is a tautology. But mathematicians don't define numbers like that.
It is a logical fallacy to say that because the probability of a proposition being true is infinitesimal, then the proposition isn't true.
Another interesting problem, discussed by minds greater than ours over the centuries. More interesting are these 2 questions.
1. Why God (if existing) allows purposeless (non teleological) evil to exist?
2. Where does the notion of evil arise?
I got a 1st on my essay regarding the 1st in Philosophy at university. Though my main subject was maths. If you like we could argue about the number of angels who'll fit on the head of a pin.Comment
-
Originally posted by BR14 View Post42
Having brought Millie in from a muddy walk earlier, I gave her a shower. As I towelled her off, I was thinking to myself: What do you get if you multiply six by nine?
...and that’s how you get 42.…Maybe we ain’t that young anymoreComment
-
Originally posted by WTFH View PostThere’s no point in having that number without knowing how you got it.
Having brought Millie in from a muddy walk earlier, I gave her a shower. As I towelled her off, I was thinking to myself: What do you get if you multiply six by nine?
...and that’s how you get 42.
Comment
-
Originally posted by BR14 View Postnah, that's 25 or 6 to 4
how many roads must a mouse travel?Always forgive your enemies; nothing annoys them so much.Comment
-
Comment
-
Originally posted by JohntheBike View Post
and don't forget hexadecimal where A + B = 21Comment
-
Comment
- Home
- News & Features
- First Timers
- IR35 / S660 / BN66
- Employee Benefit Trusts
- Agency Workers Regulations
- MSC Legislation
- Limited Companies
- Dividends
- Umbrella Company
- VAT / Flat Rate VAT
- Job News & Guides
- Money News & Guides
- Guide to Contracts
- Successful Contracting
- Contracting Overseas
- Contractor Calculators
- MVL
- Contractor Expenses
Advertisers
Contractor Services
CUK News
- Life Insurance services Yesterday 10:21
- Relevant Life Insurance Services Yesterday 10:08
- Will umbrella company regulation spark mergers and acquisitions? Yesterday 09:24
- Critical Illness Insurance for Contractors: Protect Yourself When It Matters Most Jan 14 16:26
- Relevant Life Insurance for Contractors with a Limited Company Jan 14 16:14
- Life Insurance for Contractors: Why it’s Essential Jan 14 16:09
- Guide to Income Protection Insurance for Contractors Jan 14 16:00
- Treasury minister told six actions can save contractor umbrella sector from ‘existential’ crisis Jan 14 09:40
- Critical Illness Services Jan 13 16:41
- Income Protection Services Jan 13 16:35
Comment