Why 1/0 is not infinity

Why can't we divide by zero? The answer is here! I also talk about why 1/0 is not infinity.

Category:

Education

Tags:

• infinity
• 1/0
• division by zero

[GuythePikey]

How would you illustrate a wave of the tan function as it gets near π/2, ie when sin is close to one and cos is close to zero?

[DrKevinHouston]

@GuythePikey By drawing the line of the graph tending to +/- infinity.

[leemes08]

Much simpler: if 1/0 should be infinity, why should -1/0 = 1/-0 = 1/0 be infinity but not -infinity which is NOT infinity? And one often forgets that there are no rules to calculate with infinity, not even that infinity * 0 = 0. It's getting worse when people think that e.g. for x -> infinity, 1/x * x converges to 0 because 1/x -> 0 and x -> infinity and 0 * infinity = 0... Common mistake!

[DrKevinHouston]

@leemes08 Good points! I like your -infinity= infinity argument.

[djlivingfire]

One can divide by zero when one understands the difference between static quantity (incomplete) and dynamic quantity (1! complete). Integers referring to static quantity for equation solving purposes are illusory and incomplete - but when math as a system is considered, division by zero is a process like any other complete function. In the dynamic quantity, zero and infinity are, in fact, the same.

[his1nightmare]

Well what this video states is that 1/lim x->0 is infinity, not that 1/0 is infinity, which isn't defined as infinity either but as undefined, singularity, etc.

>: 8

[DrKevinHouston]

@JustWiseon3 But surely x/x=1. So why do you say 0/0=0? After all, if 0*1=0 as you say as well, then dividing both sides by 0 should give 1.

[JustWiseon3]

@DrKevinHouston Arithmetic allows us to cancel a * (b/a) because it equals to (a/a) * b. Since a/a = 1, when a is not 0, a/a * b = b. Therefore 0 * 1/0 will never be 1, since 0/0 = 0 and 0 * 1 = 0.

[ov3rcl0cked]

In physics infinity is a recursive happening, it goes at a rate endlessly(or till the end of time), nothing at any point is known to be endless but rather know to be ever growing. So 1/0, so 0+0=0 so keep looping till you add enough 0's to get to 1, which in our system of physics and mathematics is endless, or at least until the end of time. Which for all we know could be endless.

I guess arithmetics is another story, though Scp1966 makes a good point, arithmetics only apply to finite numbers.