There is no such thing as a "real number" and the Ancient Greeks rejected infinity in its ENTIRETY. It's quite rich that the idiot acolytes of Cantor ask me to provide an integer for an object whose boundaries don't exist!!!! If you give me 3.14159..., you haven't given anything that's "infinite", you baboons!!! Wake up! Even in your bullshit mainstream math, you never actually use infinity because INFINITY CANNOT BE DONE. Infinity is not required in mathematics and never belonged in mathematics or any other field of STEM. You don't get to make up ill-formed definitions and pass your drivel on under the name of mathematics. A concept must be well-formed: www.academia.edu/45567545/There_are_no_postulates_or_axioms_in_Greek_mathematics Sound Mathematics is discoverable. Your bullshit mainstream "mathematics" is NOT discoverable because it is based on ill-formed concepts. Take me seriously or be ashamed in the future when your children and grandchildren laugh at your ignorance and stupidity. They will ridicule the lot of you mainstream apes who are known as the High Priests of Mainstream Mathematics. First learn what it means to be a number, you baboons! www.academia.edu/120915959/Arithmetic_without_numbers I give you the entire derivation in ONE page and you don't need a course on that anti-mathematical drivel of set theory or ZFC "axioms" to understand: www.academia.edu/125757733/Realisation_and_Development_of_Number_in_1_Page Join here to get access to Members Only Channel: th-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.htmljoin
No valid construction of "real number": www.academia.edu/32016659/On_Dedekind_cuts No, you can't just make up whimsical definitions from your pea-size brains. That is not mathematics. Mathematics is the abstract science of MEASURE and NUMBER. NOTHING ELSE.
Thanks for this video. I have a question: I fully get the sense of your point, but can we say: the set of real constants instead of the set of real numbers? I do understand that the concept of Set is not well-defined, but why can we not use the term constant instead of number? Would that be a problem? For example, rational constants (which are the numbers) and irrational constants (due to failed measure). Is that an issue? I will highly appreciate your kind response. Thanks in advance.
"I fully get the sense of your point, but can we say: the set of real constants instead of the set of real numbers?" If you do this, then you have to define to what precision your constant is measured up to. For example, if you choose pi accurate to 10000 trillion digits, there are still many rational numbers with the same n digits as pi in the same n places that change in the next digit, i.e., 10001 trillionth digit. Therefore, the constant would not be a **unique** number. "I do understand that the concept of Set is not well-defined, but why can we not use the term constant instead of number?" Well, we do use constants exactly as we use numbers - they are numbers, but numbers that do not represent a full measure. Let's see an example. sqrt2 = Failed Measure (square diagonal : square side) 1st measure = 1.4 2nd measure = 1.41 3rd measure = 1.414 No matter how many digits you compute, the above constants are NOT the measure of (square diagonal : square side). "Would that be a problem?" Yes, because these constants are numbers that do not represent the full measure, only an approximation. "For example, rational constants (which are the numbers) and irrational constants (due to failed measure). Is that an issue?" "Irrational constants" are still rational numbers which approximate the "irrational constants". The complete realization of number is given here: www.academia.edu/125757733/Realisation_and_Development_of_Number_in_1_Page The complete discovery of arithmetic without numbers is here: www.academia.edu/124828666/Gabriel_arithmetic_without_numbers_a_method_based_on_Thales_proportionality_theorem Algebra takes the final result a step further. It tries to measure the ratio with a common unit, which is known as the abstract unit, whose type and size is not relevant, but it functions the same way as a physical unit. The only difference is that algebra measures using an abstract unit and/or **equal** parts of the abstract unit. Geometry measures using a physical unit and/or parts of the physical unit. BTW: I like my comments because it prevents them from being hidden because others vote them down. So, there is method to my madness. :-)
So the solution to the equation x² = 2 is not a number? It is not rational and since you believe "number" to be equivalent to "rational", I assume that there is no number that solves the equation?
Exactly! There is no number solution to that equation, only an approximation of sqrt(2). Perhaps you like 1.4? Hm, maybe 1.414? Maybe more? Whatever you choose, it's not the measure of the ratio (square diagonal : square side). You got it now! Or maybe not .... Lol
False. They did have a concept for negative number even though it was not called this. For the Greeks, -x meant a lack of the quantity x, and that is the correct interpretation of "negative number".
There is no such thing as a "real number" and the Ancient Greeks rejected infinity in its ENTIRETY.
It's quite rich that the idiot acolytes of Cantor ask me to provide an integer for an object whose boundaries don't exist!!!! If you give me 3.14159..., you haven't given anything that's "infinite", you baboons!!! Wake up! Even in your bullshit mainstream math, you never actually use infinity because INFINITY CANNOT BE DONE. Infinity is not required in mathematics and never belonged in mathematics or any other field of STEM.
You don't get to make up ill-formed definitions and pass your drivel on under the name of mathematics. A concept must be well-formed:
www.academia.edu/45567545/There_are_no_postulates_or_axioms_in_Greek_mathematics
Sound Mathematics is discoverable. Your bullshit mainstream "mathematics" is NOT discoverable because it is based on ill-formed concepts.
Take me seriously or be ashamed in the future when your children and grandchildren laugh at your ignorance and stupidity. They will ridicule the lot of you mainstream apes who are known as the High Priests of Mainstream Mathematics.
First learn what it means to be a number, you baboons!
www.academia.edu/120915959/Arithmetic_without_numbers
I give you the entire derivation in ONE page and you don't need a course on that anti-mathematical drivel of set theory or ZFC "axioms" to understand:
www.academia.edu/125757733/Realisation_and_Development_of_Number_in_1_Page
Join here to get access to Members Only Channel:
th-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.htmljoin
No valid construction of "real number":
www.academia.edu/32016659/On_Dedekind_cuts
No, you can't just make up whimsical definitions from your pea-size brains. That is not mathematics.
Mathematics is the abstract science of MEASURE and NUMBER.
NOTHING ELSE.
Your ideas are very interesting. I’m inclined to believe them.
And, though I’m sure you don’t mean to be, you’re hilarious!
Thanks for this video.
I have a question:
I fully get the sense of your point, but can we say: the set of real constants instead of the set of real numbers?
I do understand that the concept of Set is not well-defined, but why can we not use the term constant instead of number? Would that be a problem?
For example, rational constants (which are the numbers) and irrational constants (due to failed measure). Is that an issue?
I will highly appreciate your kind response.
Thanks in advance.
"I fully get the sense of your point, but can we say: the set of real constants instead of the set of real numbers?"
If you do this, then you have to define to what precision your constant is measured up to. For example, if you choose pi accurate to 10000 trillion digits, there are still many rational numbers with the same n digits as pi in the same n places that change in the next digit, i.e., 10001 trillionth digit. Therefore, the constant would not be a **unique** number.
"I do understand that the concept of Set is not well-defined, but why can we not use the term constant instead of number?"
Well, we do use constants exactly as we use numbers - they are numbers, but numbers that do not represent a full measure.
Let's see an example.
sqrt2 = Failed Measure (square diagonal : square side)
1st measure = 1.4
2nd measure = 1.41
3rd measure = 1.414
No matter how many digits you compute, the above constants are NOT the measure of (square diagonal : square side).
"Would that be a problem?"
Yes, because these constants are numbers that do not represent the full measure, only an approximation.
"For example, rational constants (which are the numbers) and irrational constants (due to failed measure). Is that an issue?"
"Irrational constants" are still rational numbers which approximate the "irrational constants".
The complete realization of number is given here:
www.academia.edu/125757733/Realisation_and_Development_of_Number_in_1_Page
The complete discovery of arithmetic without numbers is here:
www.academia.edu/124828666/Gabriel_arithmetic_without_numbers_a_method_based_on_Thales_proportionality_theorem
Algebra takes the final result a step further. It tries to measure the ratio with a common unit, which is known as the abstract unit, whose type and size is not relevant, but it functions the same way as a physical unit. The only difference is that algebra measures using an abstract unit and/or **equal** parts of the abstract unit. Geometry measures using a physical unit and/or parts of the physical unit.
BTW: I like my comments because it prevents them from being hidden because others vote them down. So, there is method to my madness. :-)
If what you asked is if it is okay to use the symbols pi, sqrt2, etc. Yes, it is okay as long as one understands they are approximations.
So the solution to the equation x² = 2 is not a number? It is not rational and since you believe "number" to be equivalent to "rational", I assume that there is no number that solves the equation?
Exactly! There is no number solution to that equation, only an approximation of sqrt(2). Perhaps you like 1.4? Hm, maybe 1.414? Maybe more? Whatever you choose, it's not the measure of the ratio (square diagonal : square side). You got it now! Or maybe not .... Lol
The Greek also didn’t have negative numbers, do you think we should abandon them to?
False. They did have a concept for negative number even though it was not called this. For the Greeks, -x meant a lack of the quantity x, and that is the correct interpretation of "negative number".