Numerous teachers of mathematics will tell you that x/x = 1, (x+1)/(x+1) = 1, (x-7)/(x-7) = 1, etc.
This is not quite correct. If x = 0, then x/x does not equal one. There is no inverse for zero and hence 0/0 has no answer.
In the second example above if x = -1 we again have 0/0. In the third example if
x = +7 we again have 0/0.
Hence, (x +9)/(x+9) = 1, but x cannot equal -9 is the complete answer.
Suppose you graph y = (sine x)/x. When x = 0 we have y= (sine x)/x = 0/0. Hence at x = 0, y = 0 on the number plane we put in a discontinuous point.
Monday, 3 February 2014
Sunday, 2 February 2014
RECYCLED WATER
Some communities in Australia refuse to drink recycled water. Some people say that they will never drink recycled water.
About 2000 years ago a Roman soldier dies in a secluded part of the North African desert. His body slowly decomposes and his water molecules evaporate into the atmosphere. From there his molecules become part of the world's water cycle. After 2000 years his molecules could be in the Indian Ocean, the Pacific Ocean, your local lake, your local water supply, etc.
One day you decide to drink a litre of water from your kitchen tap (this tap could be "anywhere" in the world). What is the most probable minimum number of water molecules that you will drink which were once in this soldiers body?
Most of my students usual guess between zero and one hundred. Onto the whiteboard I put up 0, 10,100,1000,...................1,000,000,000,000. I put the numbers up in powers of ten with the last number being ten to the power of 12. My students are asked to guess the closest number to the estimated answer.
The most probable minimum number is about 20,000,000 (20M). Hence, ten to the power of seven is the closest number which they can guess.
We ALL drink recycled water. The next time you drink a can of coke (which is mainly water) try estimating the minimum number of molecules which came from that Roman soldiers body!
About 2000 years ago a Roman soldier dies in a secluded part of the North African desert. His body slowly decomposes and his water molecules evaporate into the atmosphere. From there his molecules become part of the world's water cycle. After 2000 years his molecules could be in the Indian Ocean, the Pacific Ocean, your local lake, your local water supply, etc.
One day you decide to drink a litre of water from your kitchen tap (this tap could be "anywhere" in the world). What is the most probable minimum number of water molecules that you will drink which were once in this soldiers body?
Most of my students usual guess between zero and one hundred. Onto the whiteboard I put up 0, 10,100,1000,...................1,000,000,000,000. I put the numbers up in powers of ten with the last number being ten to the power of 12. My students are asked to guess the closest number to the estimated answer.
The most probable minimum number is about 20,000,000 (20M). Hence, ten to the power of seven is the closest number which they can guess.
We ALL drink recycled water. The next time you drink a can of coke (which is mainly water) try estimating the minimum number of molecules which came from that Roman soldiers body!
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