Maths and Physics questions

[xing]

Recently, DS, Year 4, becomes very much into Maths and Physics. He is asking all sorts of questions, but some I found I need some help from experts to answer. Can anyone help answer the following questions or recommend a website/books?

1. Maths - I can prove there is a negative 0, and I can also prove there is no negative 0. Is there a negative 0?

2. Maths - Is there a number between 0.9 recursive and 1?

3. Maths - What is infinite - infinite?

4. Physics - When the light beam first comes out, what's the speed?

5. Physics - What a light particle hit glass, will it slow down?

1)-0=+0 there isn't really such a thing as -0 as they are equal. However because lots of numbers are actually rounded it can be helpful to think of a -ve 0 as meaning a number less than 0 that when rounded became 0 (particularly useful in computing).
2)No - if you added any digit onto the end of 0.9recursive it would make it a smaller number.
3)infinite - infinite is a concept not an entity so once you reach infinite you can't have more than one multiple of it.
4)light doesn't slow down unless it changes material so the same speed as when you measure it elsewhere
5)yes - assuming it has come from the air
for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at approx 200000 km/s; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 299700 km/s

1. Any negative number is the product of -1 and the number e.g. -3=3*-1 However, any number multiplied by 0 is still 0, so 0*-1=0. Therefore, theoretically, the concept of -0 exists but it is always expressed (and behaves) as 0 which is why we never write -0, or indeed think about -0.

These are amazing questions from a year 4!

3. infinity - infinity is an indeterninate form. en.m.wikipedia.org/wiki/Indeterminate_form

4. no. 0.999999… = 1.
   en.m.wikipedia.org/wiki/0.999...

5. what is your definition of positive? Afaik x is positive if x> 0 do 0 is not positive neither negative.

2. • no. Proof: x = 0.999999999 etc. 10x = 9.99999999 etc

10x - x (i.e. 9x) = 9.9999999 - 0.9999999 = 9.

9x = 9 so x = 1

Thank you for all the Answers and links.

MadAboutMathsMum -- thank for the physics answers, I did not these light particle theories, looks like I need to learn more...

Hi everyone, Can you help on a new questions?

Does the light particles build up/accelerate the speed to 3X100000000m/s ? Or travels at 3X100000000m/s constantly?

xing - do you think your son would sit through an episode of Wonders Of The Universe? The fourth episode was on light and may help him answer that question. The other series that may help and is slightly easier to manage is Neil deGrasse Tyson's new Cosmos series.

mrsmortis , we don't watch TV much. but I will note the programs you recommended. Thanks.

infinite - infinite is a concept not an entity so once you reach infinite you can't have more than one multiple of it.

Yes you can. There is an infinite number of positive numbers and an infinite number of negative numbers and an infinate number of both positve and negative that is greater than the infinate number of either positive or negative numbers.

0 is neither negative or positive and mathematics got quite a long way before anyone defined it. In early computing systems a bit was used to indicate whether a number was +ve or -ve and as computers are binary (can only have +ve or -ve) +ve and -ve zero occurred. This is why some early computerised bills were sent to people for £0 and if nothing was paid reminder and red reminders would be sent out. The computer was working properly, it just treated 0 as a positive or negative interger.

light speed is defined in a vacuum, so the speed at which light is traveling is the same whether it has just left the source or whether it is 500 miles away in a vacuum. But the speed of light does change when it travels through anything else whether that is air or glass, different substances allow light to pass at different speeds.

Has he seen Dara O'Briain's 'school of hard sums'? it's on Dave and has all sorts of interesting bits and pieces.

I would second Wonders of the Universe. My DS sat through the series at 3, absorbed. We come back to the DVDs again and again.

sashh, thank you for much for your explanation, especially the light part.

jaws5, thanks for the DVD suggestion.