Can anyone give an example in the real world where this simple mathematical relationship is perfectly correct? Hint" In order for the equation to be perfectly correct, one would need to prove that 2 entities are identical. IOW 1a exactly = 1b BoyntonStu
one bad idea plus one bad idea equals two bad ideas unless both ideas are exactly the same, in which case there is only one bad idea
thats easy haha you have one apple , i have one apple, you give me you apple... now I have two apples so one apple + one aplle = 2 apples one + one = 2
I respectfully disagree. 1 Fuji plus 1 Granny Smith equals 2 apples. Only the quantity or magnitude need be identical, and 1 = 1 per the reflexive property.
Exactly. When we categorize things, they become sufficiently equal to be counted in the same units even though they are not identical things. Hence, 1+1=2. And, as my previous example shows, things that are not physical (like "bad ideas") can only be separate entities if there are some differences to distinguish them. If you make them identical, there is no physical location difference to distinguish them, and they become one in the same thing. So if two people each come up with the same exact bad idea, and they try to add them, it doesn't work. Hence, 1+1=1 and there is only one bad idea. If each of two people come up with a different bad idea, they can indeed say that they now, together, have two bad ideas. So the idea of needing exactly identical things in order to add them is a very tricky concept.
It's the old case of dissimilar units. One man add (marries) one women gives one couple, i.e. 1 + 1 = 1 which is seemingly a nonsense, when really it is 1M + 1W = 1C where M and W are very different things (no jokes please!) and results is something different again. Dave
Dave, Exactly! All units in nature are dissimilar; electrons included. Therefore 1+1 =2 is the language of Mathematics and it never corresponds exactly to any 2 entities in reality. BoyntonStu
thats just stupid! according to you maths does not exist because "any one number + any other number = one new number" therefore 1+1 is always 1 for you
In physical science, homogeneity of equations needs to be considered. One "thing" + One "thing" (both identical) = Two things of that One "thing" = One pair of that One "thing" Thanks.
"(both identical)" That's the rub. In Math, numbers are identical, in Nature, "things" are never identical. BoyntonStu
Look up equivalence classes in maths. The same concept also appears in (the english) language and real life. Either of these can be used to demonstrate, as far as anything at all can be proven, that 1+1 = 2
In Math I agree. Mathematics is a language and not a Science. Has any Scientist ever measured a "1"? Equivalence is not identical. No 2 "things" can ever be identical simply because they cannot occupy the same place at the same time. BoyntonStu
Yes, of course. We observe that the earth has "one" satellite/moon, that our solar system has "one" sun and only "one" planet that has life forms. We note that a single-mode optical fiber has only "one" bound propagating spatial mode and use that fact to transmit high information data rates with no modal dispersion of the optical pulses. We observe that the hydrogen atom has "one" proton in the nucleus. We can detect the passage of "one" alpha particle in a bubble chamber, or with a Geiger counter. (This is not my field. I hope I got that right.) We detect the detonation of "one" nuclear explosion when a country decides to do a nuclear weapons test. Need I go on? .......... These are all examples of discrete quantities that follow from careful definition of categories/classes/groups.
Sounds like we are questioning the definition of "1". Everything is relatively defined in measurement. For example, 1 metre was historically defined by the French Academy of Sciences. It's true that in the physical world, two things can't occupy the same place at the same time; unless they are "ghosts". And mathematics is the "language" of science. Thanks.
Your examples of 'one', are they static or are they dynamic? For example, is the Sun defined for an instant in time or would it be the same Sun 1 microsecond later? Are there exactly '2' of any of them? BoyntonStu
The examples are in response to your question whether scientists have ever measured "one", so these measurements would be of relatively short duration (static). The example of the sun has been well defined for about 4.5 billion years and is expected to be true for the next 4 billion years. Even though the sun changes over time, it still fits into our category/definition for "sun" for a very long time. These examples could conceivably have "two" of them also. There are "binary" star solar systems and planets with "two" moons. There are "bi"-modal optical fibers and there is the helium atom with "two" protons in the nucleus. Also, some Japanese scientists detected "two" nuclear explosions in their country at the end of WWII. Basically, I reject your notion that things must be identical to be counted or added. Categorization of things into a fundamental class/unit is sufficient to allow us to count and add in the real world. Even the abstract mathematics of counting and addition finds roots in set theory which is fundamentally similar to the scientific approach.