40+40x0+1 ?

[minimuffy]

40 + 40 x 0 + 1 =

A- 1
B- 41
c- 0

I say its B-41 as you need to multiply then add. (from what i remember of standard grade maths the acroymym BOMDAS- brackets off, multiply, divide, add, subtract)

DH says its 1.

please tell he's wrong!

Will do

40/0 is not infinity, it is undefined.

However, re adding things to infinity you've got to love Hilbert's Hotel.
Hilbert's hotel has infinitely many rooms and they're all full. A guest comes along wanting a room. No problem, the person in room 1 moves to room 2, the person in room 2 moves to room 3 and so on. That leaves room 1 free for the new guest to stay in.

So, there are infinitely many rooms and they are all full. An infinite number of guests turn up wanting rooms. So the person in room 1 moves to room 2, the person in room 2 moves to room 4, the person in room 3 moves to room 6 and so on. As there are infinitely many even numbers, the infinitely many guests already in the hotel get a new room.
This leaves the odd numbered rooms free. As there are infinitely many odd numbers, the infinitely many new guests all can be fitted in.

I did A-level maths and I thought it was 1, never heard of BODMAS we always had brackets.

This may be why I failed A-level maths. :o
I was in the top set for GCSE though.

Indeed x tends to infinity. But at no point is x equal to infinity.

If you plotted a graph of y = 40/x, then as x gets closer to zero, then the y value gets higher and higher, the graph gets closer and closer to a vertical line as it gets closer to the y axis. Then, when x is negative, the graph suddenly reappears below the x axis. When x = 0 the graph skips a bit (an asymptote) because at that point the value of 40/x is undefined.

Look at the graph of y=1/x <a class="break-all" href="http://www.google.co.uk/imgres?q=graph+of+y%3D1/x&hl=en&safe=off&sa=X&biw=1280&bih=685&tbm=isch&prmd=imvns&tbnid=qz5X7hlE4XYF4M:&imgrefurl=hotmath.com/hotmath_help/topics/asymptotes.html&docid=HJcFNTZwe5FVQM&imgurl=hotmath.com/hotmath_help/topics/asymptotes/hyperbola.gif&w=300&h=301&ei=ZVK9TrWwEoGn8gPqxqG6BA&zoom=1&iact=rc&dur=545&sig=114332862869581834220&page=3&tbnh=142&tbnw=142&start=33&ndsp=18&ved=1t:429,r:2,s:33&tx=113&ty=46" rel="nofollow" target="_blank">here which is the same shape. What happens when x=0? It skips a bit and in that gap switches from massively positive to massively negative.

I'm in classics!!!!!!

I managed to do the sum in my OP, everything else that has me

but it's infinite giraffe - that means that it must = infinity.
that graph will never ever end - that's what infinity is

Absolutely, definitely, 41.
In the absence of brackets, you perform the multiplication first.

40+400+1 = 40+(400)+1 = 40+0+1 = 41

(40+40)0+1 = 1
(40+40)(0+1) = 80

Zero cannot be obtained unless the 0 is moved to the start or end.

Look at the graph, nickel at x=0. Is it 'equal to' positive infinity or negative infinity seeing as it approaches both positive and negative infinity as you get closer to x = 0 depending on which direction you are headed in.

It can't be equal to both. In fact it's equal to neither, it is undefined, we can't say where the graph is at x=0.

Dividing by zero is most certainly undefined. If you decide it is 'equal' to something, then all sorts of inconsistencies soon start to occur.

e.g.
If you were to state that 1/0= infinity, then you would have to agree that 1=infinity x 0. (In the same way that saying 6/2=3 is equivalent to saying 6=3x2)

But we know that 0 times anything is 0, so the conclusion would be that

1=0

Which is clearly nonsense.

Jux, no, this is set theory actually :)

nickelbabe you can add stuff to infinity - just not in this context. If we're dealing with infinite ordinals (first, second, third, ..., omega-th,...) where omega is shorthand for the smallest infinite ordinal, you find that omega + 1 is not omega. However, 1 + omega=omega.

I love it when addition gets non-commutative :o

and if anyone's confused, omega is the same as aleph zero, provided you assume the axiom of choice

You know what I love about MN? That sort of stuff coming from a fictional dachshund

Actually I'm just as in awe of anyone who understands set theory as anyone who understands number theory. You may be my new goddess

Ah, complexnumber, that buggers up my primary school explanation earlier then (repeated subtraction).

So in the repeated subtraction eg maybe it would work to say, "You can carry on subtracting forever, so your number of divisions goes off into infinity." That would introduce "tends to infinity", while your counter-example would then show you can't plough on and blithely manipulate infinity like a number.

Any holes (for primary level)?

Is it Aleph Zero not Aleph Null schnitzel? Or can it be either?

I just asked my yr8 DD. She got it wrong, but then said 'oh yes, we learned BODMAS in Yr5....but we had all forgotten it in Yr7'. Apparently when the teacher realised this, she got them to do a sum, then put it into their (school standard BODMAS-compliant) calculators whereat there were lots of cries of either 'my calculator doesn't work' or 'whaa... I can't do maths'.

DilysPrice I've always called it aleph zero myself but others call it aleph null. I think Elvis Cridlington, if he took a second career in mathematics, would probably go for aleph nothing as it has a nice ring to it. And Norman Price probably calls it aleph oops. I may start doing that myself...

Jux read this book. It's fab, and very easy to read - not too dry and textbook like. It even has a section where you have to imagine you're at kindergarten and can't yet count. My favourite set theory book ever. :)

DH has redeemed his flaky BODMAS instincts with this extremely hardcore "joke":

What's yellow and equivalent to the Axiom of Choice?
Zorn's Lemon! ??

What's purple and commutes?

An abelian grape

what's green and zingy and belongs to a non-singular algebraic variety??

This bodmas stuff is stupid, isn't it? You work out what's in the brackets first, and then work left to right with the result.