Contradictions \ldots \ldots \ldots

This is a note for discussing contradictions and sharing facts, links opinions, info and more.

  • ×0=?\infty \times 0 = ?

  • Is 10=?Is \ \frac{1}{0} = \infty ?

  • 00=1, but why?0^{0} = 1, \ but \ why?

Share more contradicting problems so we can discuss and debate upon their answer!

Note by Percy Jackson
4 months, 1 week ago

No vote yet
1 vote

  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:

  • 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.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Percy, here's my opinion on the value of 10\frac{1}{0}, and here's my general opinions on working with \infty (my comment, not the discussion).

David Stiff - 4 months, 1 week ago

Log in to reply

10=\frac{1}{0} \cancel{=} \infty as then \Rightarrow 1=0×1 = 0 \times \infty \Rightarrow 1=01 = 0

This is true for all numbers divided by 0, so division by 0 is just undefined......

Percy Jackson - 4 months, 1 week ago

Log in to reply

If 10\frac{1}{0} "is" =,= ∞, then we have an answer for ×,0∞ × ,0 which will be 1\boxed{1}

@Percy Jackson

Frisk Dreemurr - 4 months, 1 week ago

Log in to reply

But we know that 0×x0 \times x is always 00 with any value of xx.

@Hamza Anushath

Percy Jackson - 4 months, 1 week ago

Log in to reply

@Percy Jackson @Percy Jackson

Only with finite values of xx

Lâm Lê - 2 weeks ago

Log in to reply

@Lâm Lê Yes, that's also true...

Percy Jackson - 1 week, 6 days ago

Log in to reply

@Lâm Lê xx is a NUMBER and \infty is NOT a NUMBER \therefore xx alway have to be finite

Zakir Husain - 1 week, 6 days ago

Log in to reply

@Lâm Lê And if you are talking about : limx(x×0)\boxed{\lim_{x\to\infty}(x\times 0)} then, limxx×0=0\lim_{x\to\infty}x\times 0 = 0

Zakir Husain - 1 week, 6 days ago

Log in to reply

1/0 is undefined because you are basically asking what number times 0 or how many zeroes should you add so that you get 1, even if you add infinite zeroes the answer would be 0.

Siddharth Chakravarty - 4 months, 1 week ago

Log in to reply

@Hamza Anushath

If limn0nn=000=1\lim_{n\to 0}n^n=0\cancel{\Rightarrow}0^0=1

The result will be different if you include complex numbers (something like lima0limb0(a+bi)a+bi\lim_{a\to0}\lim_{b\to0}(a+bi)^{a+bi} or lima0(a+ai)a+ai\lim_{a\to0}(a+ai)^{a+ai} or lima0(ai)a\lim_{a\to0}(ai)^{a}, etc ).

00\therefore0^0 is undefined.

Also if limxaf(x)=kf(a)=k\lim_{x\to a}f(x)=k\cancel{\Rightarrow}f(a)=k

Zakir Husain - 4 months, 1 week ago

Log in to reply

@Hamza Anushath see this if you don't believe me.

Zakir Husain - 4 months, 1 week ago

Log in to reply

@Zakir Husain Link Isn't the topic still debatable?

Siddharth Chakravarty - 4 months, 1 week ago

Log in to reply

What about this? Assume 00\frac{0}{0} is undefined. Then 10=\frac{1}{0} = \infty, but 0×10 \times \infty \neq 1, since to obtain this, we would have to multiply 10\frac{1}{0} by 00, resulting in 00×1\frac{0}{0} \times 1, which would then be undefined.

David Stiff - 1 week, 5 days ago

Log in to reply

But why 10\dfrac{1}{0} must be \infty?, why not UNDEFINED\red{UNDEFINED}

Zakir Husain - 1 week, 4 days ago

Log in to reply

Also f(x)=1xf(x)=\frac{1}{x} is discontinuous at x=0x=0 so you can't give f(0)f(0) any value

Zakir Husain - 1 week, 4 days ago

Log in to reply

@Zakir Husain This is true, but only if we assume that there is both a positive and negative value of infinity. What if we have a single point of infinity where everything ends, similar to 00, where everything begins. Then we would get the situation I described in this discussion. Please note this is all speculation on my part. Definitely fun to think about!

David Stiff - 1 week, 4 days ago

Log in to reply

Percy, 0^0 is not equal to 1...

Shevy Doc - 3 months ago

Log in to reply

Yes that's just the*best *answer

Lâm Lê - 1 month, 2 weeks ago

Log in to reply

Well, I just watched a video by Eddie Woo on 00=?0^{0} = ? and he solves the question by using limits. He says that it is undefined, but it seems as if its one, so we have agreed upon that value, until we find a better solution. He shows that limx0xx=1\lim_{x \to 0} x^{x} = 1 by calculating x^x for decimals and showing that is approaches 1.

Percy Jackson - 1 week, 3 days ago

Log in to reply

(limxaf(x)=A)(f(a)=A)(\lim_{x\to a}f(x)=A)\cancel{\Rightarrow}(f(a)=A) (f(a)=A)(limxaf(x)=A)(f(a)=A){\Rightarrow}(\lim_{x\to a}f(x)=A)

Zakir Husain - 1 week, 3 days ago

Log in to reply

Also you are looking only for Real limits not Complex limits

Zakir Husain - 1 week, 3 days ago

Log in to reply

Contradiction in Probability

Zakir Husain - 5 days, 15 hours ago

Log in to reply

Haha, nice @Zakir Husain!!!

Percy Jackson - 4 days, 21 hours ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...