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Look said:My diagram is not only a picture, but it uses a linkage among visual AND symbolic reasoning.
It's still not mathematically rigorous.
Look said:My diagram is not only a picture, but it uses a linkage among visual AND symbolic reasoning.
So you are some kind of a superman.micromass said:Yes.
Look said:So you are some kind of a superman.
By your (probably) formal school of thought it is not mathematically rigorous, but this is no more than your philosophical view of mathematics, that has nothing to do with how mathematics actually can be done.micromass said:It's still not mathematically rigorous.
Look said:By your (probably) formal school of thought it is not mathematically rigorous, but this is no more than your philosophical view of mathematics, that has nothing to do with how mathematics actually can be done.
Exactly as pictures-only can be misleading so is the case about verbal-symbolic-only reasoning.micromass said:Here's another fun proof without words:
Since when being minority means that one does not doing valuable mathematics?micromass said:Then I hope you realize that all modern mathematicians agree that this is not mathematically rigorous? I mean, if you have a different philosophical view on mathematics, that's fine. But you do realize you're minority, right?
Look said:Since when being minority means that one does not doing valuable mathematics?
I hope that you realize that since there is minority, then it is not true that "all modern mathematicians agree that this is not mathematically rigorous".micromass said:Then I hope you realize that all modern mathematicians agree that this is not mathematically rigorous? I mean, if you have a different philosophical view on mathematics, that's fine. But you do realize you're minority, right?
Look said:I hope that you realize that since there is minority, then it is not true that "all modern mathematicians agree that this is not mathematically rigorous".
Now you fail by attacking me and not my argument. Is this an example of how to use rigorous mathematical reasoning?micromass said:No, since I don't count you as a modern mathematician.
Look said:If you disagree with this implementation then please show that ##a+b+c+d+...=X## doe not imply ##2X = X\sqrt{2}##.
Since you agree that 1/2+1/4+1/8+1/16...=1, then the diagram is a proof without (additional) words that 1/2+1/4+1/8+1/16...=1 implies ##2 = 1\sqrt{2}##.
Now you fail by attacking me and not my argument. Is this an example of your rigorous mathematical reasoning?
No, all you did is to use verbal-symbolic-only reasoning, as currently used by the majority of, so called, "pure" mathematicians.micromass said:And since ##2=\sqrt{2}## is false, and since I have already given a rigorous proof that ##1/2 + 1/4 + 1/8 + ... = 1##, that implies directly that your diagram proof is wrong.
Yes.micromass said:Have you published mathematical papers?
Look said:No, all you did is to use verbal-symbolic-only reasoning, as currently used by the majority of, so called, "pure" mathematicians.
By using visual AND symbolic reasoning, as I did in https://www.physicsforums.com/threa...nitiator-generator.881023/page-5#post-5542100, I rigorously prove that the acceptances that ##1/2 + 1/4 + 1/8 + ... = 1## implies directly that your verbal-symbolic-only reasoning does not hold, since ##1/2 + 1/4 + 1/8 + ... = 1## implies ##2=\sqrt{2}##.
Yes.
One can't find this error in verbal-symbolic-only reasoning by using verbal-symbolic-only reasoning.micromass said:Oh nono, You asked repeatedly in this thread and specifically a proof from real analysis. I provided you with exactly such proof. You never asked for visual reasoning.
Also, I proved the result by verbal-symbolic reasoning. Why would that method make it invalid. Where is the error in the proof?
Only if you show yours in this thread.micromass said:Care to show?
Thank you.micromass said:It's alright if you don't want to, I believe you anyway.
Look said:One can't find any error in verbal-symbolic-only reasoning by using verbal-symbolic-only reasoning.