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/sci/ - Science & Math

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7039504 No.7039504 [Reply] [Original]

Is there and infinite amount of real numbers on the number line between any two real numbers?

>> No.7039507

I think so

>> No.7039516

Yes. Let <span class="math">a \ne b[/spoiler] be real numbers. Consider the map <span class="math">n \mapsto a + \frac{b-a}{2^n} [/spoiler]. It is clearly an injective function.

>> No.7039521
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7039521

>>7039504
>Is there and infinite amount of real numbers on the number line between any two real numbers?
real numbers are bullshit. infinities in nature don't exist.

>> No.7039524

>>7039504
Yes and this is true for rational numbers too. See >>7039516

>> No.7039526

>>7039524
What about irrational numbers?

>> No.7039533

>>7039504
there are 0 real numbers on the number line between any two [subsequent] real numbers

>> No.7039536

>>7039526

Them too.

>> No.7039537

>>7039536
Thanks

>>7039533
I don't get it

>> No.7039538

>>7039521

So many things dumb about this post.

>> No.7039540

>>7039533
>muh 0.9... meme

>> No.7039594

>>7039533
This man is correct and an idiot at the same time, what an interesting superposition.

>> No.7039599

>>7039594
too bad subsequent real number doesn't make any sense.

>> No.7039607

>>7039599
That's why he is an idiot. But it's correct still.