All including theory - why including more options increases number of correct cases when all cases are given equal probability

"AB true

ABC true

ABCD true

AD true

AC true"

to avoid confusion here too, these are standards which say "when one of these is true, set is true".

the standards for truth are:

1. When one of A, B, C, D is true (Set 2 fails in most cases here)
2. When only one of A; B, C, D is true and others false (Set 2 fails in most cases here)
3. When combination of A, B, C, D is true (Set 2 fails in most cases here)
4. When only one combination of A, B, C, D is true and others false (Set 2 fails in most cases here)

In more mathematical terms:

1. When set contains one of A, B, C, D (Set 2 true in 25% cases)
2. When set contains only one of A, B, C, D (Set 2 true in 25% cases)
3. When set contains some combination of A; B, C, D (Set 2 false in most cases)
4. When set contains only one combination of A, B, C, D (Set 2 false in most cases)

So in mathematical terms, standards for truth are:

1. When set contains one of something

2. When set contains exactly something

this "something" in case of A, B, C, D has these 16 combinations;

A

B

C

D

AB

ABC

ABCD

BC

BCD

CD

D

AD

AC

ACD

ABD

BD

Check in how many cases of 1, 2 is set X which contains only A correct, and in how many cases not correct. Do not count empty as a case, but use 16 combinations given:

Got it! Let's carefully go step by step.

We have:

1. Set X = {A}
2. Standards for truth:
3. Contains one of something → True if X contains at least one element from the "something" set.
4. Contains exactly something → True if X is exactly equal to the "something" set.
5. "Something" can be any of the 16 combinations given:

Step 1: Standard 1 — "contains one of something"

We check for each "something" if X = {A} contains at least one element of it.

1. A → yes (contains A) ✅
2. B → no ❌
3. C → no ❌
4. D → no ❌
5. AB → yes (contains A) ✅
6. ABC → yes (contains A) ✅
7. ABCD → yes (contains A) ✅
8. BC → no ❌
9. BCD → no ❌
10. CD → no ❌
11. D → no ❌
12. AD → yes (contains A) ✅
13. AC → yes (contains A) ✅
14. ACD → yes (contains A) ✅
15. ABD → yes (contains A) ✅
16. BD → no ❌

✅ Count of correct (True) = 8

❌ Count of incorrect (False) = 8

Step 2: Standard 2 — "contains exactly something"

We check if X = {A} is exactly equal to each "something".

1. A → yes ✅
2. B → no ❌
3. C → no ❌
4. D → no ❌
5. AB → no ❌
6. ABC → no ❌
7. ABCD → no ❌
8. BC → no ❌
9. BCD → no ❌
10. CD → no ❌
11. D → no ❌
12. AD → no ❌
13. AC → no ❌
14. ACD → no ❌
15. ABD → no ❌
16. BD → no ❌

✅ Count of correct (True) = 1

❌ Count of incorrect (False) = 15

✅ Step 3: Summary for X = {A}

If you want, I can also draw a quick diagram showing which sets are True/False for each standard, which makes it visually obvious.

Do you want me to do that?

Now check for A, B, C, D set:

Got it! Let's carefully solve this step by step.

We have:

1. Standards for truth:
2. Set contains one of something
3. Set contains exactly something
4. Set X: contains only {A, B, C, D} (all four elements present individually).
5. 16 combinations of "something" (given):

First, let’s clean duplicates: there is D twice. So the unique 16 combinations are:

✅ 15 unique combinations. We'll proceed with these 15.

Step 1: “Contains one of something”

This is true if X has at least one element from the "something" set.

Since X = {A, B, C, D}, check each combination:

✅ All 15 combinations are correct for standard 1.

1. Correct: 15
2. Not correct: 0

Step 2: “Contains exactly something”

This is true if X is exactly equal to the "something" set.

X = {A, B, C, D}

1. Correct: 1
2. Not correct: 14

✅ Summary

If you want, I can also draw a quick Venn-style diagram showing why “contains one of” always hits but “contains exactly” rarely does—it’s very visual.

Do you want me to do that?

Other standards could be:

1. When set contains one of something

2. When set doesnt contain any of something

Let us check again.

this "something" in case of A, B, C, D has these 16 combinations;

A

B

C

D

AB

ABC

ABCD

BC

BCD

CD

D

AD

AC

ACD

ABD

BD

Check in how many cases of 1, 2 is set X which contains only A correct, and in how many cases not correct. Do not count empty as a case, but use 16 combinations given.

Got it! Let’s carefully go step by step.

We are checking standards for truth:

1. Contains one of something → True if the set contains at least one element from the "something" subset.
2. Doesn’t contain any of something → True if the set contains none of the "something" subset.

The "something" sets are the 16 combinations you listed:

You want to check these against X = {A}.

Step 1: Check “contains one of something” (Standard 1)

1. X = {A}
2. For each "something" subset S, does {A} contain at least one element of S?

We check each:

1. A → yes (contains A) ✅
2. B → no ❌
3. C → no ❌
4. D → no ❌
5. AB → yes (contains A) ✅
6. ABC → yes (contains A) ✅
7. ABCD → yes (contains A) ✅
8. BC → no ❌
9. BCD → no ❌
10. CD → no ❌
11. D → no ❌
12. AD → yes (contains A) ✅
13. AC → yes (contains A) ✅
14. ACD → yes (contains A) ✅
15. ABD → yes (contains A) ✅
16. BD → no ❌

✅ Count of correct (true) = 8

❌ Count of not correct (false) = 8

Step 2: Check “doesn’t contain any of something” (Standard 2)

1. True if X = {A} contains none of the elements in S:
2. A → contains A → ❌
3. B → does not contain B → ✅
4. C → does not contain C → ✅
5. D → does not contain D → ✅
6. AB → contains A → ❌
7. ABC → contains A → ❌
8. ABCD → contains A → ❌
9. BC → does not contain B or C → ✅
10. BCD → does not contain B, C, D → ✅
11. CD → does not contain C or D → ✅
12. D → does not contain D → ✅
13. AD → contains A → ❌
14. AC → contains A → ❌
15. ACD → contains A → ❌
16. ABD → contains A → ❌
17. BD → does not contain B or D → ✅

✅ Count of correct (true) = 7

❌ Count of not correct (false) = 9

✅ Summary Table

If you want, I can also visualize all 16 combinations against X = {A} in a small table for super-clear comparison. This makes it instantly obvious which subsets are true/false for each standard.

Do you want me to do that?

Got it! Let's carefully go step by step.

We are checking 16 given combinations of subsets of ({A, B, C, D}) against two truth standards:

1. Set contains one of something
2. Set doesn’t contain any of something

We want to see in how many cases a set X containing A, B, C, D is considered "correct" (true) or "not correct" (false) under these rules.

Step 1: List of 16 combinations

Given:

1. A
2. B
3. C
4. D
5. AB
6. ABC
7. ABCD
8. BC
9. BCD
10. CD
11. D (duplicate, let's ignore one)
12. AD
13. AC
14. ACD
15. ABD
16. BD

✅ Total: 16 unique combinations (ignoring the duplicate “D”).

Step 2: Define the standards mathematically

1. Contains one of something

1. “Something” = {A, B, C, D} (all 16 combinations are subsets of this set)
2. Any combination that has at least one element is true.
3. So all 16 combinations (non-empty) are correct.

2. Doesn’t contain any of something

1. “Something” = {A, B, C, D}
2. Only combinations with none of A, B, C, D are correct.
3. In our list, there are no empty sets, so all 16 are not correct under this standard.

✅ Step 3: Summary Table

So, for a set containing any of A, B, C, D:

1. It always satisfies standard 1.
2. It never satisfies standard 2.

If you want, I can also mark each of the 16 combinations individually as correct/incorrect for both standards, so it’s crystal clear.

Do you want me to do that?

At the end you are still left with one God. You don’t need 4 gods to create the same universe.

Yeah, atheism (Set which includes no Gods) is lower in number compared to sets which include Gods: Set 1: (Krishna), Set 2: (Zeus, Poseidon)...ect. Atheism is just 1 set, and sets containing different Gods are many. Maybe Gods created universe together, or one God created universe while other Gods just did something else.

Different religions fro different co7ntries all observed the same thing. One god creating the universe.

@Debby

False. You ignored many pagan religions.

Yeah, but you need a GOD to create a GOD, ad infinitum.

Yes Lucy, GOD is imaginary.

And yet you put so much effort into so much bunkum.

A

AB

ABC

ABCD

FXLT

BFQW

NKPY

JRFU

AABABCABCDFXLTBFQWNKPYJRFUTWATLUCY...Therefore GOD is just an imagination.

And yet you put so much effort

Its not really much effort. Mathematically, the number of empty sets is 1. the number of sets with Gods is infinite. So mathematically, theism has much more sets than atheism, and thus its mathematical probability increases. But this wasnt theism vs atheism. this was monotheism vs polytheism, or why including more options mathematically increases correct options even when we assume there are wrong choices which make set incorrect.

Sets of what?

Symbolic representations of quantity, are simply what they are.

Do you know what sets in math are?

You use sets in math 

as the fundamental building blocks for defining all other mathematical structures, from basic numbers (like the set of all integers) to complex concepts in algebra, topology, probability, and computer science, allowing for clear grouping and manipulation of objects, making them essential for logic, databases, programming, and even defining functions and relations across all disciplines. 

In Mathematics.

In Computer Science

1. Data Structures: Representing collections of unique items (like arrays, lists, or hash sets).
2. Databases: Relational calculus uses set theory to query and manage data.
3. Algorithms: Used in algorithms for searching, sorting, and verifying program termination.
4. Programming: Found in many programming languages for efficient data handling and logic. 

In Real Life & Other Sciences

1. General Grouping: Sorting living/non-living things, seasons, or physical/chemical changes in science.
2. Fuzzy Logic: Used in engineering, medicine, and business for incomplete information.
3. Defining Concepts: Clearly expressing abstract ideas in various scientific fields. 

As I stated, math or symbolic representations of quantity are what they are and cannot make an imaginary deity real, no matter how many sets one might concoct.

So you dont know what set is.

Hmmmm, the women at the Big Bang Club say that I have a set.

Are you relying on a rumour?

And you do not know the difference between sets and imagination.

Sets cannot make imagination externally real.

God mathematically exists because set which includes all other sets logically exists in math.

Therefore we can imagine any number of unknown entities and they must exist because math and Lucy say so.

So that somewhat trivialises GOD doesn't it...Makes it one in a billion GODS...Actually for as long as humans possess imagination GODS will become endless.

That is why the Bible uses a trinity to maximize the number of gods possible.

I will use the infinity and maximise possibility.

See my new thread and create a GOD or GODDESS.

As many as you like.

Are they approved by any religion?

Yes, it's referred to as Mathematical Sets.

Mathematical sets, while fundamental to modern mathematics, have significant limitations concerning logical paradoxes, structural rigidity, and inability to represent certain types of data. The primary framework, Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC), imposes strict rules to avoid paradoxes that arise from unrestricted collection

. 

Key limitations of mathematical sets include:

1. Paradoxes and Size Restrictions: Naive set theory allowed for the "set of all sets," which leads directly to Russell's paradox (a set that cannot contain itself or not contain itself). To avoid this, axiomatic systems restrict what can be considered a set, prohibiting collections that are "too big".
2. "Proper Class" Inability: Collections that are too large to be sets are called "proper classes" (e.g., the class of all groups, the class of all vector spaces, or the class of all ordinals). These cannot be treated as elements of other sets, limiting their usability in certain formal proofs.
3. Lack of Structure: A basic set is unordered and ignores the relationship between elements; it only cares if an object is inside or outside. It cannot natively represent structure like graphs, hierarchies, or continuous relationships without additional definitions.
4. Dependency on Axioms: Sets do not exist inherently; they must be derived using specific axioms. A set valid in one axiomatic system might not be valid in another, creating inconsistencies across different mathematical frameworks.
5. Independence Phenomenon: Certain statements in set theory, such as the Continuum Hypothesis, are independent of the ZFC axioms, meaning they can be neither proven nor disproven within that system.
6. Modeling Limitations: Some modern mathematical concepts, such as those found in homotopy theory or higher category theory, are not easily modeled by sets, leading some to propose alternative foundations like category theory or type theory. 

Limitations of "Limits of Sets"

While not directly about the definition of sets, the concept of a limit of a sequence of sets also has limitations. A sequence of sets does not always have a well-defined limit (convergence) unless the sets are monotonic (consistently increasing or decreasing). 

Indeed.

So you accept its limitations. Good.

 No Size Restrictions-Big Bang Club

Competing with each other must be fun.