This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
When posting on Brilliant:
Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
Markdown
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*italics* or _italics_
italics
**bold** or __bold__
bold
- bulleted - list
bulleted
list
1. numbered 2. list
numbered
list
Note: you must add a full line of space before and after lists for them to show up correctly
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# 4 spaces, and now they show
# up as a code block.
print "hello world"
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# 4 spaces, and now they show
# up as a code block.
print "hello world"
Math
Appears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3
2×3
2^{34}
234
a_{i-1}
ai−1
\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
\sin \theta
sinθ
\boxed{123}
123
Comments
In fact, in quantum physics, "negative norm" do pop up from time to time, as a consequence of mathematical computations, and physicists simply choose to eliminate or ignore these cases, saying, "it's un-physical". Kind of like eliminating cases where energy appears to be negative. It's not a "fact" that norms (aka absolute value, or modulus) is NECESSARILY always positive. We have "normed algebras" (i.e., e.g., reals, complex numbers, quaternions, octonions) that behave nicely and allow the existence of norms that are "always" positive. But then we can have sedenions which do NOT have this property, i.e., it lacks multiplicative normedness.
When one tries to make a sweeping claim that the absolute value of a thing can't ever be less than zero, a lot of potentially interesting math is being tossed out the window without the benefit of examination.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
In fact, in quantum physics, "negative norm" do pop up from time to time, as a consequence of mathematical computations, and physicists simply choose to eliminate or ignore these cases, saying, "it's un-physical". Kind of like eliminating cases where energy appears to be negative. It's not a "fact" that norms (aka absolute value, or modulus) is NECESSARILY always positive. We have "normed algebras" (i.e., e.g., reals, complex numbers, quaternions, octonions) that behave nicely and allow the existence of norms that are "always" positive. But then we can have sedenions which do NOT have this property, i.e., it lacks multiplicative normedness.
When one tries to make a sweeping claim that the absolute value of a thing can't ever be less than zero, a lot of potentially interesting math is being tossed out the window without the benefit of examination.