1. "Order structure of the real line" is plain drivel which is meaningless and irrelevant in every respect. This expression is used in order to prime your brain for intervals that are not proper intervals such as those mentioned in the Bullshit of Lebesgue Integration. 2. We don't integrate over sets, but over a distance. 3. Bounded function is also a silly term that is used when mainstream idiots want to restrict the values of a given interval to a supremum. Of course, it's obvious that one cannot integrate over an interval that has "infinitely large or small values". 4. You'll see that Rudin focuses mainly on exotic concepts that are ill-formed in the first place. He eventually arrives at the Riemann Integral on Page 26. There is no such thing as a "real number line": www.academia.edu/45471258/Is_the_real_number_line_real Dedekind Cuts and Equivalent Cauchy Sequences are not valid constructions: www.academia.edu/32016659/On_Dedekind_cuts A definite integral is the product of two arithmetic means. Download the free eBook on the Single Variable New Calculus: www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus Britannica entry wrong: www.academia.edu/108640381/The_Britannica_entry_for_Mean_Value_Theorem_is_WRONG The Mean Value Theorem ___IS___ the fundamental theorem of calculus: www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus Join here to get access to Members Only Channel: th-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.htmljoin
1. "Order structure of the real line" is plain drivel which is meaningless and irrelevant in every respect. This expression is used in order to prime your brain for intervals that are not proper intervals such as those mentioned in the Bullshit of Lebesgue Integration.
2. We don't integrate over sets, but over a distance.
3. Bounded function is also a silly term that is used when mainstream idiots want to restrict the values of a given interval to a supremum. Of course, it's obvious that one cannot integrate over an interval that has "infinitely large or small values".
4. You'll see that Rudin focuses mainly on exotic concepts that are ill-formed in the first place. He eventually arrives at the Riemann Integral on Page 26.
There is no such thing as a "real number line":
www.academia.edu/45471258/Is_the_real_number_line_real
Dedekind Cuts and Equivalent Cauchy Sequences are not valid constructions:
www.academia.edu/32016659/On_Dedekind_cuts
A definite integral is the product of two arithmetic means.
Download the free eBook on the Single Variable New Calculus:
www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus
Britannica entry wrong:
www.academia.edu/108640381/The_Britannica_entry_for_Mean_Value_Theorem_is_WRONG
The Mean Value Theorem ___IS___ the fundamental theorem of calculus:
www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
Join here to get access to Members Only Channel:
th-cam.com/channels/lBbBVLs3M-d3dNgU4Vop_A.htmljoin