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
3 weeks, 5 days ago

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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 - 3 weeks, 5 days ago

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

@Percy Jackson

Frisk Dreemurr - 3 weeks, 5 days ago

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

@Hamza Anushath

Percy Jackson - 3 weeks, 5 days ago

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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 - 3 weeks, 5 days ago

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@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 - 3 weeks, 4 days ago

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

Zakir Husain - 3 weeks, 4 days ago

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

Siddharth Chakravarty - 3 weeks, 4 days ago

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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 - 3 weeks, 1 day ago

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