Just a nonsensical calculation?

[Lucifer666]

Hey guys.

I was bored and I just started fiddling around with my scientific calculator for fun.

I wrote down the equation:
x + 1 = x
And made it solve for x.

Now, I was expecting it to say x = ∞ (infinity), since ∞ + 1 = ∞
But instead, it gave out a *very* strange answer.
x = 1.667988098 * 10^13
Which, when written normally, is 16,679,880,980,000.
That's pretty messed up, because I'm pretty sure 16,679,880,980,000 + 1 = 16,679,880,980,001

How does this work? This is just an error, right? There is no way this corresponds to the rules of mathematics.

I think that maybe since all scientific calculators give answers to 10 significant figures, (and if the number has more than 10 digits then it is written in standard form/scientific notation), then maybe adding 1 won't affect the answer that shows up on the screen, when the actual value, however, has increased by 1.

I still find it intriguing that it chooses these exact numbers, even if I make it solve for x over and over again. It doesn't make sense!

What do you guys think?

It got a bit weirder afterwards. I grabbed my brother's calculator and input the *exact* same equation and made it solve for x.
It returned: x = 2
How does that make sense at all? 3 =/= 2 !

 

[Rydian]

Combination of overflow and "clamping", methinks.

 

[PolloDiablo]

pretty much, that equation doenst make sense

2+1 can never be equal to 2
the same way.... X+1 can never be equal to X
is jut that simple

your calculator will keep popping random numbers or errors. I guess it depends on the type of calculator you use.

 

[FAST6191]

Mathematically speaking you have created gibberish. Now this is not to say it is not useful as equations that can not be solved give us lots of interesting maths (see imaginary and complex numbers and all they do for various fields and going into computing the whole p=np thing).

First case- that is probably the largest number it can handle or the largest number it got to before it decided it was in an infinite loop and broke the cycle as Rydian said

Second case- your brother's calculator probably treated it as it would be done in many programming languages

In essence you created a variable called x which it probably initialised to 0 (note many programming languages will not be so kind)
you then to told it to take x add 1 and store it back in the x variable. (x=1) (this would be the initial definition)
If you then ran the equation/solve again it would add another 1 and end up at 2

 

[Sicklyboy]

Besides the fact that that equation isn't even possible?

Let x= 1, 2, or 3.

1 + 1 = 2.
2 + 1 = 3
3 + 1 = 4

But the first digit and the answer should be the same because they're both x, which isn't possible. x + c = x + c.

x + 1 = y is valid.

 

[Lucifer666]

Well, theoretically speaking, infinity would be a valid solution for 'x', but I guess scientific calculators don't deal with infinity, because infinity has the ability to break the rules of basic algebra. For example, 2x = infinity. Divide both sides by 2 and you get x = infinity.

I tried heading over to a more intelligent calculator. Actually, it's a tool that does just about anything. Really useful. Some of you may have heard of WolframAlpha.
This is what it returned:

Which I guess, is a much better result than 1.667988098 * 10^13.

 

[FAST6191]

Yeah that would be the "proper" answer I guess (you asked does the one side did indeed equal the other).

As for infinity for the most part if you treat infinity like that (which is to say effectively just another number) you will get odd looks from mathematicians (it is why you are told to write things like as something tends to infinity the result tends to something else as opposed to when something equals infinity the result is something else).
Also for giggles have a read up on Aleph numbers aka greater infinities.