it’s like: 1+1=2, but 1+1=2+1+1=? is undefined. <–can you tell which modulus we can possibly use in this concept and into which it may result?
In the context of the equation “1+1=2+1+1=?,” if we want to explore the possibility of using a modulus to determine the result, we can consider different modulus values and see how they affect the equation.

Modulus, also known as the remainder when dividing a number by another, is often denoted by the symbol “%”. It can be used to find the remainder of a division operation.

Let’s consider a few examples:

1. Modulus 3:
Using modulus 3, we would evaluate remainders when dividing numbers by 3. Therefore:
1 + 1 = 2 % 3 + 1 % 3 + 1 % 3
= 2 + 1 + 1
= 4

2. Modulus 4:
Using modulus 4, we would evaluate remainders when dividing numbers by 4. Therefore:
1 + 1 = 2 % 4 + 1 % 4 + 1 % 4
= 2 + 1 + 1
= 4

3. Modulus 5:
Using modulus 5, we would evaluate remainders when dividing numbers by 5. Therefore:
1 + 1 = 2 % 5 + 1 % 5 + 1 % 5
= 2 + 1 + 1
= 4

In each of these examples, regardless of the modulus value used, the resulting sum remains the same as the original equation, which is 4.

It’s important to note that modulus does not directly impact the addition operation itself but rather affects the remainders in divisions. Therefore, in the context of this equation, using various modulus values does not change the result.
I mean “mod” and modulus together with all possible logical operators.
I apologize for the misunderstanding. If you are referring to using the modulus operation (often denoted as “mod”) along with logical operators in the context of the equation “1+1=2+1+1=?”, we can explore different possibilities.

Using the modulus operation, we can consider applying it to the numbers in the equation and then incorporating logical operators like addition, subtraction, multiplication, or division to manipulate the resulting values.

Here are some examples using different logical operators:

1. Modulo addition:
(1 + 1) mod 2 + ((2 + 1 + 1) mod 2)
= 0 + (4 mod 2)
= 0 + 0
= 0

2. Modulo subtraction:
(1 + 1) mod 2 - ((2 + 1 + 1) mod 2)
= 0 - (4 mod 2)
= 0 - 0
= 0

3. Modulo multiplication:
(1 + 1) mod 2 * ((2 + 1 + 1) mod 2)
= 0 * (4 mod 2)
= 0 * 0
= 0

4. Modulo division:
(1 + 1) mod 2 / ((2 + 1 + 1) mod 2)
= 0 / (4 mod 2)
= 0 / 0 (undefined division by zero)

In these examples, we used the modulo operation along with different logical operations. However, in all cases, the result appears to be 0 or undefined due to the specific values involved in the equation.

It’s important to note that in traditional arithmetic operations, logical operators like addition, subtraction, multiplication, or division are typically not used in the same expression as the modulo operation. The usage of these operators together would require a specific context or definition to give them meaning and determine the desired outcome.
any other ideas to get a result?
Certainly! Here are a few additional ideas to explore in order to obtain a result for the equation “1+1=2+1+1=?” or to manipulate the expression further:

1. Exponentiation:
You could try raising both sides of the equation to a certain power:
(1+1)^2 = (2+1+1)^2
Square both sides:
4 = 6^2
Simplify:
4 = 36

2. Factorial:
You could apply the factorial operation to the expression:
(1+1)! = (2+1+1)!
2! = 4!
2 = 24

3. Square root or nth root:
Take the square root (or an nth root) of both sides:
√(1+1) = √(2+1+1)
√2 = √4
√2 = 2

4. Trigonometric functions:
Apply trigonometric functions to the expression:
sin(1+1) = sin(2+1+1)
sin(2) = sin(4)
0.9092974 = -0.7568025

Please note that these manipulations are unconventional and may not follow traditional mathematical operations or rules. Additionally, the outcomes generated through these non-standard manipulations might not have a direct connection to the original equation or align with conventional mathematical principles.

These are just some imaginative possibilities to explore, and the results may not be meaningful in the usual mathematical sense. The goal here is to experiment and think creatively while considering different mathematical concepts and operations.
not sure to which values to stick. generally, I like this Trigonometrical outputs, but practically it will be better to use a more understandable and simplified approach overally.
Understood. If you prefer a more understandable and simplified approach, it would be best to avoid deviating too far from conventional mathematical principles. Instead, you can focus on exploring patterns, relationships, or transformations within the existing equation while using known operations.

One approach could be to examine the equation from a different perspective and look for meaningful relations or transformations. For example, you could consider:

1. Rearranging terms:
Rearrange the equation to group like terms together or simplify the expression:
1 + 1 = 2 + (1 + 1)
= 2 + 2

2. Combining like terms:
Combine the similar terms on each side of the equation:
1 + 1 = 4

3. Applying arithmetic operations:
Apply basic arithmetic operations to simplify the equation:
2 = 4

From this simplified perspective, the equation suggests an inconsistency or contradiction, as 2 does not equal 4. This observation highlights a potential error or mistake in the original reasoning or assumptions.

In summary, focusing on rearranging terms, combining like terms, and applying basic arithmetic operations can lead to a more understandable and simplified approach when exploring patterns or relationships within the equation.
what about some "delta’ in action?
If you’d like to incorporate the concept of “delta” into the equation, you can consider analyzing the differences between certain values or terms. The symbol Δ often represents the concept of “change” or “difference” in mathematics.

For example, let’s examine the differences between the terms in the equation “1+1=2+1+1=?”:

Δ(1+1) = Δ(2+1+1)
2 - 2 = 4 - 2

Here, we subtract the terms on both sides to examine the differences between them. Simplifying further, we have:

0 = 2

However, this result is inconsistent, as 0 does not equal 2. Therefore, incorporating the concept of delta in this context does not yield a meaningful or valid solution.

Keep in mind that the usage of delta depends on the specific context and equation you are working with. In some cases, it can reveal insights about changes or differences between values, but in other cases, it may not provide a significant contribution or lead to a clear solution.
what about some "delta’ mixed with “lambda” in action?
If you would like to explore the combination of “delta” and “lambda” in the context of the equation “1+1=2+1+1=?,” we can consider various possibilities.

The symbol Δ typically represents the concept of “difference” or “change” in mathematics, while λ is often used to denote a parameter or variable.

One approach could be to introduce a lambda parameter to represent the difference between terms. For example:

1 + 1 = 2 + λ + λ

Here, λ represents the difference in value between the last two terms (1+1) and (2+1+1).

If we assume that λ has a specific value, let’s say λ = 2, we can substitute it into the equation:

1 + 1 = 2 + 2 + 2

Simplifying, we have:

2 = 6

However, this result is inconsistent, as 2 does not equal 6. Therefore, this particular approach of combining delta with lambda does not lead to a valid solution or meaningful outcome in this context.

It’s important to note that the combination of delta with lambda (or any other mathematical symbols) would depend on the specific context and definitions assigned to them. While these symbols can be used creatively in various mathematical contexts, it’s essential to ensure that they align with established mathematical principles and interpretations to yield meaningful results.
try to implement some other scientific terms to it in combination. maybe some astrophysics?